%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "1.59", %%% date = "04 July 2024", %%% time = "12:24:04 MDT", %%% filename = "talg.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 581 4148", %%% URL = "https://www.math.utah.edu/~beebe", %%% checksum = "18571 35222 200434 1762584", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "ACM Transactions on Algorithms; bibliography; %%% TALG", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a COMPLETE BibTeX bibliography for %%% ACM Transactions on Algorithms (CODEN ????, %%% ISSN 1549-6325), covering all journal issues %%% from 2005 -- date. %%% %%% At version 1.59, the COMPLETE journal %%% coverage looked like this: %%% %%% 2005 ( 20) 2012 ( 57) 2019 ( 55) %%% 2006 ( 37) 2013 ( 21) 2020 ( 54) %%% 2007 ( 52) 2014 ( 37) 2021 ( 37) %%% 2008 ( 66) 2015 ( 20) 2022 ( 41) %%% 2009 ( 54) 2016 ( 74) 2023 ( 39) %%% 2010 ( 66) 2017 ( 38) 2024 ( 27) %%% 2011 ( 41) 2018 ( 53) %%% %%% Article: 889 %%% %%% Total entries: 889 %%% %%% The journal Web page can be found at: %%% %%% http://talg.acm.org/ %%% %%% The journal table of contents pages are at: %%% %%% http://www.acm.org/talg/ %%% http://portal.acm.org/browse_dl.cfm?idx=J982 %%% https://dl.acm.org/loi/talg %%% %%% Qualified subscribers can retrieve the full %%% text of recent articles in PDF form. %%% %%% The initial draft was extracted from the ACM %%% Web pages. %%% %%% ACM copyrights explicitly permit abstracting %%% with credit, so article abstracts, keywords, %%% and subject classifications have been %%% included in this bibliography wherever %%% available. Article reviews have been %%% omitted, until their copyright status has %%% been clarified. %%% %%% bibsource keys in the bibliography entries %%% below indicate the entry originally came %%% from the computer science bibliography %%% archive, even though it has likely since %%% been corrected and updated. %%% %%% URL keys in the bibliography point to %%% World Wide Web locations of additional %%% information about the entry. %%% %%% BibTeX citation tags are uniformly chosen %%% as name:year:abbrev, where name is the %%% family name of the first author or editor, %%% year is a 4-digit number, and abbrev is a %%% 3-letter condensation of important title %%% words. Citation tags were automatically %%% generated by software developed for the %%% BibNet Project. %%% %%% In this bibliography, entries are sorted in %%% publication order, using ``bibsort -byvolume.'' %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ====================================================================

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%%% ==================================================================== %%% Acknowledgement abbreviations:

@String{ack-nhfb= "Nelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, FAX: +1 801 581 4148, e-mail: \path|beebe@math.utah.edu|, \path|beebe@acm.org|, \path|beebe@computer.org| (Internet), URL: \path|https://www.math.utah.edu/~beebe/|"}

%%% ==================================================================== %%% Journal abbreviations:

@String{j-TALG= "ACM Transactions on Algorithms"}

%%% ==================================================================== %%% Bibliography entries:

@Article{Gabow:2005:EF, author = "Harold N. Gabow", title = "{Editor}'s foreword", journal = j-TALG, volume = "1", number = "1", pages = "1--1", month = jul, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Yuster:2005:FSM, author = "Raphael Yuster and Uri Zwick", title = "Fast sparse matrix multiplication", journal = j-TALG, volume = "1", number = "1", pages = "2--13", month = jul, year = "2005", CODEN = "????", DOI = "https://doi.org/10.1145/1077464.1077466", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Let $A$ and $B$ be two $ n \times n$ matrices over a ring $R$ (e.g., the reals or the integers) each containing at most $m$ nonzero elements. We present a new algorithm that multiplies $A$ and $B$ using $ O(m^{0.7}n^{1.2} + n^2 + o(1))$ algebraic operations (i.e., multiplications, additions and subtractions) over $R$. The na{\"\i}ve matrix multiplication algorithm, on the other hand, may need to perform $ \Omega (m n)$ operations to accomplish the same task. For $ m \leq n^{1.14}$, the new algorithm performs an almost optimal number of only $ n^2 + o(1)$ operations. For $ m \leq n^{1.68}$, the new algorithm is also faster than the best known matrix multiplication algorithm for dense matrices which uses $ O(n^{2.38})$ algebraic operations. The new algorithm is obtained using a surprisingly straightforward combination of a simple combinatorial idea and existing fast rectangular matrix multiplication algorithms. We also obtain improved algorithms for the multiplication of more than two sparse matrices. As the known fast rectangular matrix multiplication algorithms are far from being practical, our result, at least for now, is only of theoretical value.", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Edmonds:2005:MAL, author = "Jeff Edmonds and Kirk Pruhs", title = "A maiden analysis of longest wait first", journal = j-TALG, volume = "1", number = "1", pages = "14--32", month = jul, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Demaine:2005:FPA, author = "Erik D. Demaine and Fedor V. Fomin and Mohammadtaghi Hajiaghayi and Dimitrios M. Thilikos", title = "Fixed-parameter algorithms for $ (k, r)$-center in planar graphs and map graphs", journal = j-TALG, volume = "1", number = "1", pages = "33--47", month = jul, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Adler:2005:PMM, author = "Micah Adler and Dan Rubenstein", title = "Pricing multicasting in more flexible network models", journal = j-TALG, volume = "1", number = "1", pages = "48--73", month = jul, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Even:2005:NDP, author = "Guy Even and Guy Kortsarz and Wolfgang Slany", title = "On network design problems: fixed cost flows and the covering {Steiner} problem", journal = j-TALG, volume = "1", number = "1", pages = "74--101", month = jul, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Alstrup:2005:BBC, author = "Stephen Alstrup and Thore Husfeldt and Theis Rauhe and Mikkel Thorup", title = "Black box for constant-time insertion in priority queues (note)", journal = j-TALG, volume = "1", number = "1", pages = "102--106", month = jul, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Vinkemeier:2005:LTA, author = "Doratha E. Drake Vinkemeier and Stefan Hougardy", title = "A linear-time approximation algorithm for weighted matchings in graphs", journal = j-TALG, volume = "1", number = "1", pages = "107--122", month = jul, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Grabner:2005:ALC, author = "Peter J. Grabner and Clemens Heuberger and Helmut Prodinger and J{\"o}rg M. Thuswaldner", title = "Analysis of linear combination algorithms in cryptography", journal = j-TALG, volume = "1", number = "1", pages = "123--142", month = jul, year = "2005", CODEN = "????", DOI = "https://doi.org/10.1145/1077464.1077473", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Several cryptosystems rely on fast calculations of linear combinations in groups. One way to achieve this is to use joint signed binary digit expansions of small ``weight.'' We study two algorithms, one based on nonadjacent forms of the coefficients of the linear combination, the other based on a certain joint sparse form specifically adapted to this problem. Both methods are sped up using the sliding windows approach combined with precomputed lookup tables. We give explicit and asymptotic results for the number of group operations needed, assuming uniform distribution of the coefficients. Expected values, variances and a central limit theorem are proved using generating functions. Furthermore, we provide a new algorithm that calculates the digits of an optimal expansion of pairs of integers from left to right. This avoids storing the whole expansion, which is needed with the previously known right-to-left methods, and allows an online computation.", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cechlarova:2005:GSR, author = "Katar{\'\i}na Cechl{\'a}rov{\'a} and Tam{\'a}s Fleiner", title = "On a generalization of the stable roommates problem", journal = j-TALG, volume = "1", number = "1", pages = "143--156", month = jul, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Khuller:2005:PC, author = "Samir Khuller", title = "Problems column", journal = j-TALG, volume = "1", number = "1", pages = "157--159", month = jul, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Johnson:2005:NCC, author = "David S. Johnson", title = "The {NP}-completeness column", journal = j-TALG, volume = "1", number = "1", pages = "160--176", month = jul, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Janson:2005:IDL, author = "Svante Janson", title = "Individual displacements for linear probing hashing with different insertion policies", journal = j-TALG, volume = "1", number = "2", pages = "177--213", month = oct, year = "2005", CODEN = "????", DOI = "https://doi.org/10.1145/1103963.1103964", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:56 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the distribution of the individual displacements in hashing with linear probing for three different versions: First Come, Last Come and Robin Hood. Asymptotic distributions and their moments are found when the size of the hash table tends to infinity with the proportion of occupied cells converging to some $ \alpha $, $ 0 < \alpha < 1 $. (In the case of Last Come, the results are more complicated and less complete than in the other cases.) We also show, using the diagonal Poisson transform studied by Poblete, Viola and Munro, that exact expressions for finite $m$ and $n$ can be obtained from the limits as $ m, n \rightarrow \infty $. We end with some results, conjectures and questions about the shape of the limit distributions. These have some relevance for computer applications.", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Viola:2005:EDI, author = "Alfredo Viola", title = "Exact distribution of individual displacements in linear probing hashing", journal = j-TALG, volume = "1", number = "2", pages = "214--242", month = oct, year = "2005", CODEN = "????", DOI = "https://doi.org/10.1145/1103963.1103965", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:56 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This paper studies the distribution of individual displacements for the standard and the Robin Hood linear probing hashing algorithms. When a table of size $m$ has $n$ elements, the distribution of the search cost of a random element is studied for both algorithms. Specifically, exact distributions for fixed $m$ and $n$ are found as well as when the table is $ \alpha $-full, and $ \alpha $ strictly smaller than 1. Moreover, for full tables, limit laws for both algorithms are derived.", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Alstrup:2005:MIF, author = "Stephen Alstrup and Jacob Holm and Mikkel Thorup and Kristian De Lichtenberg", title = "Maintaining information in fully dynamic trees with top trees", journal = j-TALG, volume = "1", number = "2", pages = "243--264", month = oct, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:56 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Jothi:2005:AAC, author = "Raja Jothi and Balaji Raghavachari", title = "Approximation algorithms for the capacitated minimum spanning tree problem and its variants in network design", journal = j-TALG, volume = "1", number = "2", pages = "265--282", month = oct, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:56 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Elkin:2005:CAS, author = "Michael Elkin", title = "Computing almost shortest paths", journal = j-TALG, volume = "1", number = "2", pages = "283--323", month = oct, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:56 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Carvalho:2005:VAE, author = "Marcelo H. {De Carvalho} and Joseph Cheriyan", title = "An {$ O(V E) $} algorithm for ear decompositions of matching-covered graphs", journal = j-TALG, volume = "1", number = "2", pages = "324--337", month = oct, year = "2005", CODEN = "????", DOI = "https://doi.org/10.1145/1103963.1103969", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:56 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Goel:2005:AMF, author = "Ashish Goel and Adam Meyerson and Serge Plotkin", title = "Approximate majorization and fair online load balancing", journal = j-TALG, volume = "1", number = "2", pages = "338--349", month = oct, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:56 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chrobak:2005:GAM, author = "Marek Chrobak and Petr Kolman and Ji{\v{r}}{\'\i} Sgall", title = "The greedy algorithm for the minimum common string partition problem", journal = j-TALG, volume = "1", number = "2", pages = "350--366", month = oct, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:56 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Sawada:2006:GRF, author = "Joe Sawada", title = "Generating rooted and free plane trees", journal = j-TALG, volume = "2", number = "1", pages = "1--13", month = jan, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Fri May 26 08:40:43 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hegde:2006:FSE, author = "Rajneesh Hegde", title = "Finding $3$-shredders efficiently", journal = j-TALG, volume = "2", number = "1", pages = "14--43", month = jan, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Fri May 26 08:40:43 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gramm:2006:PMA, author = "Jens Gramm and Jiong Guo and Rolf Niedermeier", title = "Pattern matching for arc-annotated sequences", journal = j-TALG, volume = "2", number = "1", pages = "44--65", month = jan, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Fri May 26 08:40:43 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hassin:2006:MGV, author = "Refael Hassin and Asaf Levin", title = "The minimum generalized vertex cover problem", journal = j-TALG, volume = "2", number = "1", pages = "66--78", month = jan, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Fri May 26 08:40:43 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Epstein:2006:OSS, author = "Leah Epstein and Rob {Van Stee}", title = "Online scheduling of splittable tasks", journal = j-TALG, volume = "2", number = "1", pages = "79--94", month = jan, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Fri May 26 08:40:43 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gonzalez:2006:MTC, author = "Teofilo F. Gonzalez and Joseph Y.-T. Leung and Michael Pinedo", title = "Minimizing total completion time on uniform machines with deadline constraints", journal = j-TALG, volume = "2", number = "1", pages = "95--115", month = jan, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Fri May 26 08:40:43 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gandhi:2006:IRD, author = "Rajiv Gandhi and Magn{\'u}s M. Halld{\'o}rsson and Guy Kortsarz and Hadas Shachnai", title = "Improved results for data migration and open shop scheduling", journal = j-TALG, volume = "2", number = "1", pages = "116--129", month = jan, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Fri May 26 08:40:43 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", note = "See corrigendum \cite{Gandhi:2013:CIR}.", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Khuller:2006:PC, author = "Samir Khuller", title = "Problems column", journal = j-TALG, volume = "2", number = "1", pages = "130--134", month = jan, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Fri May 26 08:40:43 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Korsh:2006:LGC, author = "James Korsh and Paul Lafollette", title = "A loopless {Gray} code for rooted trees", journal = j-TALG, volume = "2", number = "2", pages = "135--152", month = apr, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Wed Aug 23 05:38:18 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Alon:2006:ACS, author = "Noga Alon and Dana Moshkovitz and Shmuel Safra", title = "Algorithmic construction of sets for {$k$}-restrictions", journal = j-TALG, volume = "2", number = "2", pages = "153--177", month = apr, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Wed Aug 23 05:38:18 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Lau:2006:BRG, author = "Lap Chi Lau", title = "Bipartite roots of graphs", journal = j-TALG, volume = "2", number = "2", pages = "178--208", month = apr, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Wed Aug 23 05:38:18 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Agarwal:2006:EAB, author = "Pankaj K. Agarwal and Boris Aronov and Vladlen Koltun", title = "Efficient algorithms for bichromatic separability", journal = j-TALG, volume = "2", number = "2", pages = "209--227", month = apr, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Wed Aug 23 05:38:18 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Epstein:2006:SU, author = "Leah Epstein and Rob {Van Stee}", title = "This side up!", journal = j-TALG, volume = "2", number = "2", pages = "228--243", month = apr, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Wed Aug 23 05:38:18 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Huo:2006:MMF, author = "Yumei Huo and Joseph Y.-T. Leung", title = "Minimizing mean flow time for {UET} tasks", journal = j-TALG, volume = "2", number = "2", pages = "244--262", month = apr, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Wed Aug 23 05:38:18 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hassin:2006:RST, author = "Refael Hassin and Danny Segev", title = "Robust subgraphs for trees and paths", journal = j-TALG, volume = "2", number = "2", pages = "263--281", month = apr, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Wed Aug 23 05:38:18 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Azar:2006:IAC, author = "Yossi Azar and Yossi Richter", title = "An improved algorithm for {CIOQ} switches", journal = j-TALG, volume = "2", number = "2", pages = "282--295", month = apr, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Wed Aug 23 05:38:18 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Berend:2006:CMP, author = "Daniel Berend and Amir Sapir", title = "The cyclic multi-peg {Tower of Hanoi}", journal = j-TALG, volume = "2", number = "3", pages = "297--317", month = jul, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Thu Sep 21 08:13:30 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Drmota:2006:RFA, author = "Michael Drmota and Helmut Prodinger", title = "The register function for $t$-ary trees", journal = j-TALG, volume = "2", number = "3", pages = "318--334", month = jul, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Thu Sep 21 08:13:30 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Kowalik:2006:OBL, author = "Lukasz Kowalik and Maciej Kurowski", title = "Oracles for bounded-length shortest paths in planar graphs", journal = j-TALG, volume = "2", number = "3", pages = "335--363", month = jul, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Thu Sep 21 08:13:30 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Katriel:2006:OTO, author = "Irit Katriel and Hans L. Bodlaender", title = "Online topological ordering", journal = j-TALG, volume = "2", number = "3", pages = "364--379", month = jul, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Thu Sep 21 08:13:30 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Duncan:2006:OCG, author = "Christian A. Duncan and Stephen G. Kobourov and V. S. Anil Kumar", title = "Optimal constrained graph exploration", journal = j-TALG, volume = "2", number = "3", pages = "380--402", month = jul, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Thu Sep 21 08:13:30 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Raman:2006:FFP, author = "Venkatesh Raman and Saket Saurabh and C. R. Subramanian", title = "Faster fixed parameter tractable algorithms for finding feedback vertex sets", journal = j-TALG, volume = "2", number = "3", pages = "403--415", month = jul, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Thu Sep 21 08:13:30 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Jansen:2006:AAS, author = "Klaus Jansen and Hu Zhang", title = "An approximation algorithm for scheduling malleable tasks under general precedence constraints", journal = j-TALG, volume = "2", number = "3", pages = "416--434", month = jul, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Thu Sep 21 08:13:30 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Feigenbaum:2006:SMC, author = "Joan Feigenbaum and Yuval Ishai and Tal Malkin and Kobbi Nissim and Martin J. Strauss and Rebecca N. Wright", title = "Secure multiparty computation of approximations", journal = j-TALG, volume = "2", number = "3", pages = "435--472", month = jul, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Thu Sep 21 08:13:30 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Johnson:2006:NCC, author = "David S. Johnson", title = "The {NP}-completeness column: {The} many limits on approximation", journal = j-TALG, volume = "2", number = "3", pages = "473--489", month = jul, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Thu Sep 21 08:13:30 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Lopez-Ortiz:2006:F, author = "Alejandro L{\'o}pez-Ortiz and J. Ian Munro", title = "Foreword", journal = j-TALG, volume = "2", number = "4", pages = "491--491", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Eppstein:2006:QAM, author = "David Eppstein", title = "Quasiconvex analysis of multivariate recurrence equations for backtracking algorithms", journal = j-TALG, volume = "2", number = "4", pages = "492--509", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Geary:2006:SOT, author = "Richard F. Geary and Rajeev Raman and Venkatesh Raman", title = "Succinct ordinal trees with level-ancestor queries", journal = j-TALG, volume = "2", number = "4", pages = "510--534", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Mendelson:2006:MPQ, author = "Ran Mendelson and Robert E. Tarjan and Mikkel Thorup and Uri Zwick", title = "Melding priority queues", journal = j-TALG, volume = "2", number = "4", pages = "535--556", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Baswana:2006:ADO, author = "Surender Baswana and Sandeep Sen", title = "Approximate distance oracles for unweighted graphs in expected {$ O(n^2) $} time", journal = j-TALG, volume = "2", number = "4", pages = "557--577", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Demetrescu:2006:EAD, author = "Camil Demetrescu and Giuseppe F. Italiano", title = "Experimental analysis of dynamic all pairs shortest path algorithms", journal = j-TALG, volume = "2", number = "4", pages = "578--601", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Irving:2006:RMM, author = "Robert W. Irving and Telikepalli Kavitha and Kurt Mehlhorn and Dimitrios Michail and Katarzyna E. Paluch", title = "Rank-maximal matchings", journal = j-TALG, volume = "2", number = "4", pages = "602--610", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Foschini:2006:WIE, author = "Luca Foschini and Roberto Grossi and Ankur Gupta and Jeffrey Scott Vitter", title = "When indexing equals compression: {Experiments} with compressing suffix arrays and applications", journal = j-TALG, volume = "2", number = "4", pages = "611--639", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Alon:2006:GAO, author = "Noga Alon and Baruch Awerbuch and Yossi Azar and Niv Buchbinder and Joseph (Seffi) Naor", title = "A general approach to online network optimization problems", journal = j-TALG, volume = "2", number = "4", pages = "640--660", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Evans:2006:OSV, author = "William Evans and David Kirkpatrick", title = "Optimally scheduling video-on-demand to minimize delay when sender and receiver bandwidth may differ", journal = j-TALG, volume = "2", number = "4", pages = "661--678", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Beier:2006:CES, author = "Rene Beier and Artur Czumaj and Piotr Krysta and Berthold V{\"o}cking", title = "Computing equilibria for a service provider game with (Im)perfect information", journal = j-TALG, volume = "2", number = "4", pages = "679--706", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Moore:2006:GQF, author = "Cristopher Moore and Daniel Rockmore and Alexander Russell", title = "Generic quantum {Fourier} transforms", journal = j-TALG, volume = "2", number = "4", pages = "707--723", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Archer:2007:FPM, author = "Aaron Archer and {\'E}va Tardos", title = "Frugal path mechanisms", journal = j-TALG, volume = "3", number = "1", pages = "??--??", month = feb, year = "2007", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bhatia:2007:AAB, author = "Randeep Bhatia and Julia Chuzhoy and Ari Freund and Joseph (Seffi) Naor", title = "Algorithmic aspects of bandwidth trading", journal = j-TALG, volume = "3", number = "1", pages = "??--??", month = feb, year = "2007", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Carmo:2007:QPI, author = "Renato Carmo and Tom{\'a}s Feder and Yoshiharu Kohayakawa and Eduardo Laber and Rajeev Motwani and Liadan O'Callaghan and Rina Panigrahy and Dilys Thomas", title = "Querying priced information in databases: {The} conjunctive case", journal = j-TALG, volume = "3", number = "1", pages = "??--??", month = feb, year = "2007", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ciriani:2007:DSS, author = "Valentina Ciriani and Paolo Ferragina and Fabrizio Luccio and S. Muthukrishnan", title = "A data structure for a sequence of string accesses in external memory", journal = j-TALG, volume = "3", number = "1", pages = "??--??", month = feb, year = "2007", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cormode:2007:SED, author = "Graham Cormode and S. Muthukrishnan", title = "The string edit distance matching problem with moves", journal = j-TALG, volume = "3", number = "1", pages = "??--??", month = feb, year = "2007", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The edit distance between two strings $S$ and $R$ is defined to be the minimum number of character inserts, deletes, and changes needed to convert $R$ to S. Given a text string $t$ of length $n$, and a pattern string $p$ of length $m$, informally, the string edit distance matching problem is to compute the smallest edit distance between $p$ and substrings of $t$. We relax the problem so that: (a) we allow an additional operation, namely, substring moves; and (b) we allow approximation of this string edit distance. Our result is a near-linear time deterministic algorithm to produce a factor of $ O(\log n \log \star n)$ approximation to the string edit distance with moves. This is the first known significantly subquadratic algorithm for a string edit distance problem in which the distance involves nontrivial alignments. Our results are obtained by embedding strings into $ L_1$ vector space using a simplified parsing technique, which we call edit-sensitive parsing (ESP).", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Czumaj:2007:TBW, author = "Artur Czumaj and Berthold V{\"o}cking", title = "Tight bounds for worst-case equilibria", journal = j-TALG, volume = "3", number = "1", pages = "??--??", month = feb, year = "2007", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Elkin:2007:IAR, author = "Michael Elkin and Guy Kortsarz", title = "An improved algorithm for radio broadcast", journal = j-TALG, volume = "3", number = "1", pages = "??--??", month = feb, year = "2007", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Eppstein:2007:FSI, author = "David Eppstein", title = "Foreword to special issue on {SODA 2002}", journal = j-TALG, volume = "3", number = "1", pages = "??--??", month = feb, year = "2007", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hershberger:2007:DSS, author = "John Hershberger and Subhash Suri and Amit Bhosle", title = "On the difficulty of some shortest path problems", journal = j-TALG, volume = "3", number = "1", pages = "??--??", month = feb, year = "2007", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Pandurangan:2007:EBB, author = "Gopal Pandurangan and Eli Upfal", title = "Entropy-based bounds for online algorithms", journal = j-TALG, volume = "3", number = "1", pages = "??--??", month = feb, year = "2007", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Voronenko:2007:MMC, author = "Yevgen Voronenko and Markus P{\"u}schel", title = "Multiplierless multiple constant multiplication", journal = j-TALG, volume = "3", number = "2", pages = "11:1--11:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240234", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A variable can be multiplied by a given set of fixed-point constants using a multiplier block that consists exclusively of additions, subtractions, and shifts. The generation of a multiplier block from the set of constants is known as the multiple constant multiplication (MCM) problem. Finding the optimal solution, namely, the one with the fewest number of additions and subtractions, is known to be NP-complete. We propose a new algorithm for the MCM problem, which produces solutions that require up to 20\% less additions and subtractions than the best previously known algorithm. At the same time our algorithm, in contrast to the closest competing algorithm, is not limited by the constant bitwidths. We present our algorithm using a unifying formal framework for the best, graph-based MCM algorithms and provide a detailed runtime analysis and experimental evaluation. We show that our algorithm can handle problem sizes as large as 100 32-bit constants in a time acceptable for most applications. The implementation of the new algorithm is available at \path =www.spiral.net=.", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Addition chains; directed graph; FIR filter; fixed-point arithmetic; strength reduction", } @Article{Chern:2007:PCR, author = "Hua-Huai Chern and Michael Fuchs and Hsien-Kuei Hwang", title = "Phase changes in random point quadtrees", journal = j-TALG, volume = "3", number = "2", pages = "12:1--12:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240235", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show that a wide class of linear cost measures (such as the number of leaves) in random $d$-dimensional point quadtrees undergo a change in limit laws: If the dimension $ d = 1, \ldots, 8 $, then the limit law is normal; if $ d \geq 9 $ then there is no convergence to a fixed limit law. Stronger approximation results such as convergence rates and local limit theorems are also derived for the number of leaves, additional phase changes being unveiled. Our approach is new and very general, and also applicable to other classes of search trees. A brief discussion of Devroye's grid trees (covering $m$-ary search trees and quadtrees as special cases) is given. We also propose an efficient numerical procedure for computing the constants involved to high precision.", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "analysis in distribution of algorithms; Asymptotic transfer; central limit theorems; depth; differential equations; grid trees; local limit theorems; Mellin transforms; page usage; phase transitions; quadtrees; total path length", } @Article{Demaine:2007:RDS, author = "Erik D. Demaine and John Iacono and Stefan Langerman", title = "Retroactive data structures", journal = j-TALG, volume = "3", number = "2", pages = "13:1--13:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240236", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce a new data structuring paradigm in which operations can be performed on a data structure not only in the present, but also in the past. In this new paradigm, called retroactive data structures, the historical sequence of operations performed on the data structure is not fixed. The data structure allows arbitrary insertion and deletion of operations at arbitrary times, subject only to consistency requirements. We initiate the study of retroactive data structures by formally defining the model and its variants. We prove that, unlike persistence, efficient retroactivity is not always achievable. Thus, we present efficient retroactive data structures for queues, doubly ended queues, priority queues, union-find, and decomposable search structures.", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "History; persistence; point location; rollback; time travel", } @Article{Hayward:2007:IAW, author = "Ryan B. Hayward and Jeremy P. Spinrad and R. Sritharan", title = "Improved algorithms for weakly chordal graphs", journal = j-TALG, volume = "3", number = "2", pages = "14:1--14:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240237", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We use a new structural theorem on the presence of two-pairs in weakly chordal graphs to develop improved algorithms. For the recognition problem, we reduce the time complexity from {$ O(m n^2) $} to {$ O(m^2) $} and the space complexity from {$ O(n^3) $} to {$ O(m + n) $}, and also produce a hole or antihole if the input graph is not weakly chordal. For the optimization problems, the complexity of the clique and coloring problems is reduced from {$ O(m n^2) $} to {$ O(n^3) $} and the complexity of the independent set and clique cover problems is improved from {$ O(n^4) $} to {$ O(m n) $}. The space complexity of our optimization algorithms is {$ O(m + n) $}.", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "coloring; graph algorithms; Perfect graphs; recognition; weakly chordal", } @Article{Kavitha:2007:SSM, author = "Telikepalli Kavitha and Kurt Mehlhorn and Dimitrios Michail and Katarzyna E. Paluch", title = "Strongly stable matchings in time {$ O(n m) $} and extension to the hospitals-residents problem", journal = j-TALG, volume = "3", number = "2", pages = "15:1--15:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240238", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "An instance of the stable marriage problem is an undirected bipartite graph {$ G = (X \cup W, E) $} with linearly ordered adjacency lists with ties allowed in the ordering. A matching {$M$} is a set of edges, no two of which share an endpoint. An edge {$ e = (a, b) \in E \setminus M $} is a blocking edge for {$M$} if {$a$} is either unmatched or strictly prefers {$b$} to its partner in {$M$}, and {$b$} is unmatched, strictly prefers {$a$} to its partner in {$M$}, or is indifferent between them. A matching is strongly stable if there is no blocking edge with respect to it. We give an {$ O(n m) $} algorithm for computing strongly stable matchings, where {$n$} is the number of vertices and {$m$} the number of edges. The previous best algorithm had running time {$ O(m^2) $}. We also study this problem in the hospitals-residents setting, which is a many-to-one extension of the aforementioned problem. We give an {$ O(m \sum_{h \in H} p_h) $} algorithm for computing a strongly stable matching in the hospitals-residents problem, where {$ p_h $} is the quota of a hospital {$h$}. The previous best algorithm had running time {$ O(m^2) $}.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Bipartite matching; level maximal; stable marriage; strong stability", } @Article{Bagchi:2007:DSR, author = "Amitabha Bagchi and Amitabh Chaudhary and David Eppstein and Michael T. Goodrich", title = "Deterministic sampling and range counting in geometric data streams", journal = j-TALG, volume = "3", number = "2", pages = "16:1--16:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240239", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present memory-efficient deterministic algorithms for constructing $ \epsilon $-nets and $ \epsilon $-approximations of streams of geometric data. Unlike probabilistic approaches, these deterministic samples provide guaranteed bounds on their approximation factors. We show how our deterministic samples can be used to answer approximate online iceberg geometric queries on data streams. We use these techniques to approximate several robust statistics of geometric data streams, including Tukey depth, simplicial depth, regression depth, the Thiel-Sen estimator, and the least median of squares. Our algorithms use only a polylogarithmic amount of memory, provided the desired approximation factors are at least inverse-polylogarithmic. We also include a lower bound for noniceberg geometric queries.", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Data streams; epsilon nets; geometric data; iceberg queries; range counting; robust statistics; sampling; streaming algorithms", } @Article{Arya:2007:SEB, author = "Sunil Arya and Theocharis Malamatos and David M. Mount", title = "A simple entropy-based algorithm for planar point location", journal = j-TALG, volume = "3", number = "2", pages = "17:1--17:17", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240240", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a planar polygonal subdivision {$S$}, point location involves preprocessing this subdivision into a data structure so that given any query point {$q$}, the cell of the subdivision containing {$q$} can be determined efficiently. Suppose that for each cell {$z$} in the subdivision, the probability $ p_z $ that a query point lies within this cell is also given. The goal is to design the data structure to minimize the average search time. This problem has been considered before, but existing data structures are all quite complicated. It has long been known that the entropy {$H$} of the probability distribution is the dominant term in the lower bound on the average-case search time. In this article, we show that a very simple modification of a well-known randomized incremental algorithm can be applied to produce a data structure of expected linear size that can answer point-location queries in {$ O(H) $} average time. We also present empirical evidence for the practical efficiency of this approach.", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "entropy; expected-case complexity; Point location; polygonal subdivision; randomized algorithms; trapezoidal maps", } @Article{Kauers:2007:ADZ, author = "Manuel Kauers", title = "An algorithm for deciding zero equivalence of nested polynomially recurrent sequences", journal = j-TALG, volume = "3", number = "2", pages = "18:1--18:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240241", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce the class of nested polynomially recurrent sequences which includes a large number of sequences that are of combinatorial interest. We present an algorithm for deciding zero equivalence of these sequences, thereby providing a new algorithm for proving identities among combinatorial sequences: In order to prove an identity, decide by the algorithm whether the difference of lefthand-side and righthand-side is identically zero. This algorithm is able to treat mathematical objects which are not covered by any other known symbolic method for proving combinatorial identities. Despite its theoretical flavor and high complexity, an implementation of the algorithm can be successfully applied to nontrivial examples.", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "combinatorial sequences; nested polynomially recurrent sequences; Symbolic computation; zero equivalence", } @Article{Amir:2007:DTS, author = "Amihood Amir and Gad M. Landau and Moshe Lewenstein and Dina Sokol", title = "Dynamic text and static pattern matching", journal = j-TALG, volume = "3", number = "2", pages = "19:1--19:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240242", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we address a new version of dynamic pattern matching. The dynamic text and static pattern matching problem is the problem of finding a static pattern in a text that is continuously being updated. The goal is to report all new occurrences of the pattern in the text after each text update. We present an algorithm for solving the problem where the text update operation is changing the symbol value of a text location. Given a text of length $n$ and a pattern of length $m$, our algorithm preprocesses the text in time {$ O(n \log \log m) $}, and the pattern in time {$ O(m \log m) $}. The extra space used is {$ O(n + m \log m) $}. Following each text update, the algorithm deletes all prior occurrences of the pattern that no longer match, and reports all new occurrences of the pattern in the text in {$ O(\log \log m) $} time. We note that the complexity is not proportional to the number of pattern occurrences, since all new occurrences can be reported in a succinct form.", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "border trees; Dynamic text; static pattern", } @Article{Ferragina:2007:CRS, author = "Paolo Ferragina and Giovanni Manzini and Veli M{\"a}kinen and Gonzalo Navarro", title = "Compressed representations of sequences and full-text indexes", journal = j-TALG, volume = "3", number = "2", pages = "20:1--20:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240243", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a sequence {$ S = s_1 s_2 \ldots s_n $} of integers smaller than {$ r = O(\polylog (n)) $}, we show how {$S$} can be represented using {$ n H_0 (S) + o(n) $} bits, so that we can know any {$ s_q $}, as well as answer rank and select queries on {$S$}, in constant time. {$ H_0 (S) $} is the zero-order empirical entropy of {$S$} and {$ n H_0 (S) $} provides an information-theoretic lower bound to the bit storage of any sequence {$S$} via a fixed encoding of its symbols. This extends previous results on binary sequences, and improves previous results on general sequences where those queries are answered in {$ O(\log r) $} time. For larger {$r$}, we can still represent {$S$} in {$ n H_0 (S) + o(n \log r) $} bits and answer queries in {$ O(\log r / \log \log n) $} time.\par Another contribution of this article is to show how to combine our compressed representation of integer sequences with a compression boosting technique to design compressed full-text indexes that scale well with the size of the input alphabet {$ \Sigma $}. Specifically, we design a variant of the FM-index that indexes a string {$ T[1, n] $} within {$ n H_k(T) + o(n) $} bits of storage, where {$ H_k(T) $} is the {$k$} th-order empirical entropy of {$T$}. This space bound holds simultaneously for all {$ k \leq \alpha \log | \Sigma | n $}, constant {$ 0 < \alpha < 1 $}, and {$ | \Sigma | = O(\polylog (n)) $}. This index counts the occurrences of an arbitrary pattern {$ P[1, p] $} as a substring of {$T$} in {$ O(p) $} time; it locates each pattern occurrence in {$ O(\log 1 + \varepsilon n) $} time for any constant {$ 0 < \varepsilon < 1 $}; and reports a text substring of length {$ \ell $} in {$ O(\ell + \log 1 + \varepsilon n) $} time.\par Compared to all previous works, our index is the first that removes the alphabet-size dependance from all query times, in particular, counting time is linear in the pattern length. Still, our index uses essentially the same space of the {$k$} th-order entropy of the text {$T$}, which is the best space obtained in previous work. We can also handle larger alphabets of size {$ | \Sigma | = O(n \beta) $}, for any {$ 0 < \beta < 1 $}, by paying {$ o(n \log | \Sigma |) $} extra space and multiplying all query times by {$ O(\log | \Sigma | / \log \log n) $}.", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Burrows--Wheeler transform; compression boosting; entropy; rank and select; text compression; Text indexing; wavelet tree", } @Article{Chan:2007:CID, author = "Ho-Leung Chan and Wing-Kai Hon and Tak-Wah Lam and Kunihiko Sadakane", title = "Compressed indexes for dynamic text collections", journal = j-TALG, volume = "3", number = "2", pages = "21:1--21:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240244", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Let {$T$} be a string with {$n$} characters over an alphabet of constant size. A recent breakthrough on compressed indexing allows us to build an index for {$T$} in optimal space (i.e., {$ O(n) $} bits), while supporting very efficient pattern matching [Ferragina and Manzini 2000; Grossi and Vitter 2000]. Yet the compressed nature of such indexes also makes them difficult to update dynamically.\par This article extends the work on optimal-space indexing to a dynamic collection of texts. Our first result is a compressed solution to the library management problem, where we show an index of {$ O(n) $} bits for a text collection {$L$} of total length {$n$}, which can be updated in {$ O(| T | \log n) $} time when a text {$T$} is inserted or deleted from {$L$}; also, the index supports searching the occurrences of any pattern {$P$} in all texts in {$L$} in {$ O(|P| \log n + {\rm occ} \log 2 n) $} time, where {\rm occ} is the number of occurrences.\par Our second result is a compressed solution to the dictionary matching problem, where we show an index of {$ O(d) $} bits for a pattern collection {$D$} of total length {$d$}, which can be updated in {$ O(|P| \log 2 d) $} time when a pattern {$P$} is inserted or deleted from {$D$}; also, the index supports searching the occurrences of all patterns of {$D$} in any text {$T$} in {$ O((|T| + {\rm occ}) \log 2 d) $} time. When compared with the {$ O(d \log d) $}-bit suffix-tree-based solution of Amir et al. [1995], the compact solution increases the query time by roughly a factor of {$ \log d $} only.\par The solution to the dictionary matching problem is based on a new compressed representation of a suffix tree. Precisely, we give an {$ O(n) $}-bit representation of a suffix tree for a dynamic collection of texts whose total length is {$n$}, which supports insertion and deletion of a text {$T$} in {$ O(|T| \log 2 n) $} time, as well as all suffix tree traversal operations, including forward and backward suffix links. This work can be regarded as a generalization of the compressed representation of static texts. In the study of the aforementioned result, we also derive the first {$ O(n) $}-bit representation for maintaining {$n$} pairs of balanced parentheses in {$ O(\log n / \log \log n) $} time per operation, matching the time complexity of the previous {$ O(n \log n) $}-bit solution.", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Compressed suffix tree; string matching", } @Article{Boyar:2007:RWO, author = "Joan Boyar and Lene M. Favrholdt", title = "The relative worst order ratio for online algorithms", journal = j-TALG, volume = "3", number = "2", pages = "22:1--22:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240245", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We define a new measure for the quality of online algorithms, the relative worst order ratio, using ideas from the max/max ratio [Ben-David and Borodin 1994] and from the random order ratio [Kenyon 1996]. The new ratio is used to compare online algorithms directly by taking the ratio of their performances on their respective worst permutations of a worst-case sequence.\par Two variants of the bin packing problem are considered: the classical bin packing problem, where the goal is to fit all items in as few bins as possible, and the dual bin packing problem, which is the problem of maximizing the number of items packed in a fixed number of bins. Several known algorithms are compared using this new measure, and a new, simple variant of first-fit is proposed for dual bin packing.\par Many of our results are consistent with those previously obtained with the competitive ratio or the competitive ratio on accommodating sequences, but new separations and easier proofs are found.", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "bin packing; dual bin packing; Online; quality measure; relative worst order ratio", } @Article{Becchetti:2007:SCM, author = "L. Becchetti and J. K{\"o}nemann and S. Leonardi and M. P{\'a}al", title = "Sharing the cost more efficiently: {Improved} approximation for multicommodity rent-or-buy", journal = j-TALG, volume = "3", number = "2", pages = "23:1--23:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240246", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the multicommodity rent-or-buy (MROB) network design problems, we are given a network together with a set of $k$ terminal pairs $ (s_1, t_1), \ldots, (s_k, t_k) $. The goal is to provision the network so that a given amount of flow can be shipped between $ s_i $ and $ t_i $ for all $ 1 \leq i \leq k $ simultaneously. In order to provision the network, one can either rent capacity on edges at some cost per unit of flow, or buy them at some larger fixed cost. Bought edges have no incremental, flow-dependent cost. The overall objective is to minimize the total provisioning cost.\par Recently, Gupta et al. [2003a] presented a 12-approximation for the MROB problem. Their algorithm chooses a subset of the terminal pairs in the graph at random and then buys the edges of an approximate Steiner forest for these pairs. This technique had previously been introduced [Gupta et al. 2003b] for the single-sink rent-or-buy network design problem.\par In this article we give a 6.828-approximation for the MROB problem by refining the algorithm of Gupta et al. and simplifying their analysis. The improvement in our article is based on a more careful adaptation and simplified analysis of the primal-dual algorithm for the Steiner forest problem due to Agrawal et al. [1995]. Our result significantly reduces the gap between the single-sink and multisink case.", acknowledgement = ack-nhfb, articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; cost sharing; network design; Steiner forests", } @Article{Johnson:2007:NCC, author = "David S. Johnson", title = "The {NP}-completeness column: {Finding} needles in haystacks", journal = j-TALG, volume = "3", number = "2", pages = "24:1--24:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240247", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This is the 26th edition of a column that covers new developments in the theory of NP-completeness. The presentation is modeled on that which M. R. Garey and I used in our book ``Computers and Intractability: A Guide to the Theory of NP-Completeness,'' W. H. Freeman {\&} Co., New York, 1979, hereinafter referred to as ``[G{\&}J].'' Previous columns, the first 23 of which appeared in J. Algorithms, will be referred to by a combination of their sequence number and year of appearance, e.g., ``Column 1 [1981].'' Full bibliographic details on the previous columns, as well as downloadable unofficial versions of them, can be found at \path =http://www.research.att.com/~dsj/columns/=. This column discusses the question of whether finding an object can be computationally difficult even when we know that the object exists.", acknowledgement = ack-nhfb, articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "fixed point; game theory; local search; Nash equilibrium; PLS; PPAD", } @Article{Feng:2007:FAS, author = "Jianxing Feng and Daming Zhu", title = "Faster algorithms for sorting by transpositions and sorting by block interchanges", journal = j-TALG, volume = "3", number = "3", pages = "25:1--25:14", month = aug, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1273340.1273341", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:11 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we present a new data structure, called the permutation tree, to improve the running time of sorting permutation by transpositions and sorting permutation by block interchanges. The existing 1.5-approximation algorithm for sorting permutation by transpositions has time complexity {$ O(n^{3 / 2} \sqrt {\log n}) $}. By means of the permutation tree, we can improve this algorithm to achieve time complexity {$ O(n \log n) $}. We can also improve the algorithm for sorting permutation by block interchanges to take its time complexity from {$ O(n^2) $} down to {$ O(n \log n) $}.", acknowledgement = ack-nhfb, articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Block interchange; genome; permutation; time complexity; transposition; tree", } @Article{Gupta:2007:CPD, author = "Himanshu Gupta and Rephael Wenger", title = "Constructing pairwise disjoint paths with few links", journal = j-TALG, volume = "3", number = "3", pages = "26:1--26:??", month = aug, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1273340.1273342", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:11 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Let {$P$} be a simple polygon and let {$ \{ (u_1, u{\prime }_1), (u_2, u{\prime }_2), \ldots, (u_m, u{\prime }_m) \} $} be a set of {$m$} pairs of distinct vertices of {$P$}, where for every distinct {$ i, j \leq m $}, there exist pairwise disjoint (nonintersecting) paths connecting {$ u_i $} to {$ u \prime_i $} and $ u_j $ to $ u \prime_j $. We wish to construct $m$ pairwise disjoint paths in the interior of {$P$} connecting {$ u_i $} to {$ u \prime_i $} for {$ i = 1, \ldots, m $}, with a minimal total number of line segments. We give an approximation algorithm that constructs such a set of paths using {$ O(M) $} line segments in {$ O(n \log m + M \log m) $} time, where {$M$} is the number of line segments in the optimal solution and {$n$} is the size of the polygon.", acknowledgement = ack-nhfb, articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "isomorphic triangulations; Link paths; noncrossing; polygon", } @Article{Chekuri:2007:MDF, author = "Chandra Chekuri and Marcelo Mydlarz and F. Bruce Shepherd", title = "Multicommodity demand flow in a tree and packing integer programs", journal = j-TALG, volume = "3", number = "3", pages = "27:1--27:??", month = aug, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1273340.1273343", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:11 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider requests for capacity in a given tree network {$ T = (V, E) $} where each edge {$e$} of the tree has some integer capacity {$ u_e $}. Each request {$f$} is a node pair with an integer demand $ d_f $ and a profit $ w_f $ which is obtained if the request is satisfied. The objective is to find a set of demands that can be feasibly routed in the tree and which provides a maximum profit. This generalizes well-known problems, including the knapsack and $b$-matching problems.\par When all demands are 1, we have the integer multicommodity flow problem. Garg et al. [1997] had shown that this problem is NP-hard and gave a 2-approximation algorithm for the cardinality case (all profits are 1) via a primal-dual algorithm. Our main result establishes that the integrality gap of the natural linear programming relaxation is at most 4 for the case of arbitrary profits. Our proof is based on coloring paths on trees and this has other applications for wavelength assignment in optical network routing.\par We then consider the problem with arbitrary demands. When the maximum demand $ d_{\rm max} $ is at most the minimum edge capacity $ u_{\rm min} $, we show that the integrality gap of the LP is at most 48. This result is obtained by showing that the integrality gap for the demand version of such a problem is at most 11.542 times that for the unit-demand case. We use techniques of Kolliopoulos and Stein [2004, 2001] to obtain this. We also obtain, via this method, improved algorithms for line and ring networks. Applications and connections to other combinatorial problems are discussed.", acknowledgement = ack-nhfb, articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithm; Integer multicommodity flow; integrality gap; packing integer program; tree", } @Article{Bar-Noy:2007:WSR, author = "Amotz Bar-Noy and Richard E. Ladner and Tami Tamir", title = "Windows scheduling as a restricted version of bin packing", journal = j-TALG, volume = "3", number = "3", pages = "28:1--28:??", month = aug, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1273340.1273344", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:11 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a sequence of $n$ positive integers $ w_1, w_2, \ldots, w_n $ that are associated with the items $ 1, 2, \ldots n $, respectively. In the windows scheduling problem, the goal is to schedule all the items (equal-length information pages) on broadcasting channels such that the gap between two consecutive appearances of page $i$ on any of the channels is at most $ w_i $ slots (a slot is the transmission time of one page). In the unit-fractions bin packing problem, the goal is to pack all the items in bins of unit size where the size (width) of item $i$ is $ 1 / w_i $. The optimization objective is to minimize the number of channels or bins. In the offline setting, the sequence is known in advance, whereas in the online setting, the items arrive in order and assignment decisions are irrevocable. Since a page requires at least $ 1 / w_i $ of a channel's bandwidth, it follows that windows scheduling without migration (i.e., all broadcasts of a page must be from the same channel) is a restricted version of unit-fractions bin packing.\par Let {$ H = \lceil \sum_{i = 1}^n (1 / w_i) $} be the bandwidth lower bound on the required number of bins (channels). The best-known offline algorithm for the windows scheduling problem used {$ H + O(\ln H) $} channels. This article presents an offline algorithm for the unit-fractions bin packing problem with at most {$ H + 1 $} bins. In the online setting, this article presents algorithms for both problems with {$ H + O(\sqrt {H}) $} channels or bins, where the one for the unit-fractions bin packing problem is simpler. On the other hand, this article shows that already for the unit-fractions bin packing problem, any online algorithm must use at least {$ H + \Omega (\ln H) $} bins. For instances in which the window sizes form a divisible sequence, an optimal online algorithm is presented. Finally, this article includes a new NP-hardness proof for the windows scheduling problem.", acknowledgement = ack-nhfb, articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithms; bin-packing; online algorithms; Periodic scheduling", } @Article{Hazay:2007:APM, author = "Carmit Hazay and Moshe Lewenstein and Dina Sokol", title = "Approximate parameterized matching", journal = j-TALG, volume = "3", number = "3", pages = "29:1--29:??", month = aug, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1273340.1273345", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:11 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Two equal length strings $s$ and $ s \prime $, over alphabets {$ \Sigma s $} and {$ \Sigma s \prime $}, parameterize match if there exists a bijection {$ \pi : \Sigma s \rightarrow \Sigma s \prime $} such that {$ \pi (s) = s \prime $}, where {$ \pi (s) $} is the renaming of each character of {$s$} via $ \pi $. Parameterized matching is the problem of finding all parameterized matches of a pattern string $p$ in a text $t$, and approximate parameterized matching is the problem of finding at each location a bijection $ \pi $ that maximizes the number of characters that are mapped from $p$ to the appropriate $ |p| $-length substring of $t$.\par Parameterized matching was introduced as a model for software duplication detection in software maintenance systems and also has applications in image processing and computational biology. For example, approximate parameterized matching models image searching with variable color maps in the presence of errors.\par We consider the problem for which an error threshold, $k$, is given, and the goal is to find all locations in $t$ for which there exists a bijection $ \pi $ which maps $p$ into the appropriate $ |p| $-length substring of $t$ with at most $k$ mismatched mapped elements. Our main result is an algorithm for this problem with {$ O(n k^{1.5} + m k \log m) $} time complexity, where {$ m = | p | $} and {$ n = | t | $}. We also show that when {$ | p | = | t | = m $}, the problem is equivalent to the maximum matching problem on graphs, yielding a {$ O(m + k^{1.5}) $} solution.", acknowledgement = ack-nhfb, articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Hamming distance; maximum matching; mismatch pair; parameterize match", } @Article{Halldorsson:2007:IAR, author = "Magn{\'u}s M. Halld{\'o}rsson and Kazuo Iwama and Shuichi Miyazaki and Hiroki Yanagisawa", title = "Improved approximation results for the stable marriage problem", journal = j-TALG, volume = "3", number = "3", pages = "30:1--30:??", month = aug, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1273340.1273346", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:11 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The stable marriage problem has recently been studied in its general setting, where both ties and incomplete lists are allowed. It is NP-hard to find a stable matching of maximum size, while any stable matching is a maximal matching and thus trivially we can obtain a 2-approximation algorithm.\par In this article, we give the first nontrivial result for approximation of factor less than two. Our algorithm achieves an approximation ratio of {$ 2 / (1 + L - 2) $} for instances in which only men have ties of length at most {$L$}. When both men and women are allowed to have ties but the lengths are limited to two, then we show a ratio of {$ 13 / 7 ( < 1.858) $}. We also improve the lower bound on the approximation ratio to {$ 21 / 19 ( > 1.1052) $}.", acknowledgement = ack-nhfb, articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; incomplete lists; stable marriage problem; ties", } @Article{Indyk:2007:NNP, author = "Piotr Indyk and Assaf Naor", title = "Nearest-neighbor-preserving embeddings", journal = j-TALG, volume = "3", number = "3", pages = "31:1--31:??", month = aug, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1273340.1273347", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:11 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article we introduce the notion of nearest-neighbor-preserving embeddings. These are randomized embeddings between two metric spaces which preserve the (approximate) nearest-neighbors. We give two examples of such embeddings for Euclidean metrics with low ``intrinsic'' dimension. Combining the embeddings with known data structures yields the best-known approximate nearest-neighbor data structures for such metrics.", acknowledgement = ack-nhfb, articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "dimensionality reduction; doubling spaces; embeddings; Nearest neighbor", } @Article{Even-Dar:2007:CTN, author = "Eyal Even-Dar and Alex Kesselman and Yishay Mansour", title = "Convergence time to {Nash} equilibrium in load balancing", journal = j-TALG, volume = "3", number = "3", pages = "32:1--32:??", month = aug, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1273340.1273348", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:11 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the number of steps required to reach a pure Nash equilibrium in a load balancing scenario where each job behaves selfishly and attempts to migrate to a machine which will minimize its cost. We consider a variety of load balancing models, including identical, restricted, related, and unrelated machines. Our results have a crucial dependence on the weights assigned to jobs. We consider arbitrary weights, integer weights, $k$ distinct weights, and identical (unit) weights. We look both at an arbitrary schedule (where the only restriction is that a job migrates to a machine which lowers its cost) and specific efficient schedulers (e.g., allowing the largest weight job to move first). A by-product of our results is establishing a connection between various scheduling models and the game-theoretic notion of potential games. We show that load balancing in unrelated machines is a generalized ordinal potential game, load balancing in related machines is a weighted potential game, and load balancing in related machines and unit weight jobs is an exact potential game.", acknowledgement = ack-nhfb, articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "convergence time; game theory; Nash equilibrium", } @Article{Andrews:2007:RSM, author = "Matthew Andrews and Lisa Zhang", title = "Routing and scheduling in multihop wireless networks with time-varying channels", journal = j-TALG, volume = "3", number = "3", pages = "33:1--33:??", month = aug, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1273340.1273349", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:11 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study routing and scheduling in multihop wireless networks. When data is transmitted from its source node to its destination node it may go through other wireless nodes as intermediate hops. The data transmission is node constrained, that is, every node can transmit data to at most one neighboring node per time step. The transmission rates are time varying as a result of changing wireless channel conditions.\par In this article, we assume that data arrivals and transmission rates are governed by an adversary. The power of the adversary is limited by an admissibility condition which forbids the adversary from overloading any wireless node a priori. The node-constrained transmission and time-varying nature of the transmission rates make our model different from and harder than the standard adversarial queueing model which relates to wireline networks.\par For the case in which the adversary specifies the paths that the data must follow, we design scheduling algorithms that ensure network stability. These algorithms try to give priority to the data that is closest to its source node. However, at each time step only a subset of the data queued at a node is eligible for scheduling. One of our algorithms is fully distributed.\par For the case in which the adversary does not dictate the data paths, we show how to route data so that the admissibility condition is satisfied. We can then schedule data along the chosen paths using our stable scheduling algorithms.", acknowledgement = ack-nhfb, articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "routing; Scheduling; stability; time-varying; wireless network", } @Article{Naor:2007:NAP, author = "Moni Naor and Udi Wieder", title = "Novel architectures for {P2P} applications: {The} continuous-discrete approach", journal = j-TALG, volume = "3", number = "3", pages = "34:1--34:??", month = aug, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1273340.1273350", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:11 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We propose a new approach for constructing P2P networks based on a dynamic decomposition of a continuous space into cells corresponding to servers. We demonstrate the power of this approach by suggesting two new P2P architectures and various algorithms for them. The first serves as a DHT (distributed hash table) and the other is a dynamic expander network. The DHT network, which we call Distance Halving, allows logarithmic routing and load while preserving constant degrees. It offers an optimal tradeoff between degree and path length in the sense that degree $d$ guarantees a path length of {$ O(\log d n) $}. Another advantage over previous constructions is its relative simplicity. A major new contribution of this construction is a dynamic caching technique that maintains low load and storage, even under the occurrence of hot spots. Our second construction builds a network that is guaranteed to be an expander. The resulting topologies are simple to maintain and implement. Their simplicity makes it easy to modify and add protocols. A small variation yields a DHT which is robust against random Byzantine faults. Finally we show that, using our approach, it is possible to construct any family of constant degree graphs in a dynamic environment, though with worse parameters. Therefore, we expect that more distributed data structures could be designed and implemented in a dynamic environment.", acknowledgement = ack-nhfb, articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Peer-to-peer networks; routing", } @Article{Khuller:2007:PC, author = "Samir Khuller", title = "Problems column", journal = j-TALG, volume = "3", number = "3", pages = "35:1--35:??", month = aug, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1273340.1273351", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:11 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "35", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gabow:2007:ISS, author = "H. N. Gabow and Michael A. Bender and Martin Farach-Colton", title = "Introduction to {SODA} 2002 and 2003 special issue", journal = j-TALG, volume = "3", number = "4", pages = "36:1--36:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290673", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "36", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Aspnes:2007:SG, author = "James Aspnes and Gauri Shah", title = "Skip graphs", journal = j-TALG, volume = "3", number = "4", pages = "37:1--37:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290674", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Skip graphs are a novel distributed data structure, based on skip lists, that provide the full functionality of a balanced tree in a distributed system where resources are stored in separate nodes that may fail at any time. They are designed for use in searching peer-to-peer systems, and by providing the ability to perform queries based on key ordering, they improve on existing search tools that provide only hash table functionality. Unlike skip lists or other tree data structures, skip graphs are highly resilient, tolerating a large fraction of failed nodes without losing connectivity. In addition, simple and straightforward algorithms can be used to construct a skip graph, insert new nodes into it, search it, and detect and repair errors within it introduced due to node failures.", acknowledgement = ack-nhfb, articleno = "37", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "overlay networks; Peer-to-peer; skip lists", } @Article{Han:2007:OPS, author = "Yijie Han", title = "Optimal parallel selection", journal = j-TALG, volume = "3", number = "4", pages = "38:1--38:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290675", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present an optimal parallel selection algorithm on the EREW PRAM. This algorithm runs in {$ O(\log n) $} time with {$ n / \log n $} processors. This complexity matches the known lower bound for parallel selection on the EREW PRAM model. We therefore close this problem which has been open for more than a decade.", acknowledgement = ack-nhfb, articleno = "38", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "EREW PRAM; Parallel algorithms; selection", } @Article{Bansal:2007:MWF, author = "Nikhil Bansal and Kedar Dhamdhere", title = "Minimizing weighted flow time", journal = j-TALG, volume = "3", number = "4", pages = "39:1--39:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290676", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problem of minimizing the total weighted flow time on a single machine with preemptions. We give an online algorithm that is {$ O(k) $}-competitive for {$k$} weight classes. This implies an {$ O(\log W) $}-competitive algorithm, where {$W$} is the maximum to minimum ratio of weights. This algorithm also implies an {$ O(\log n + \log P) $}-approximation ratio for the problem, where {$P$} is the ratio of the maximum to minimum job size and {$n$} is the number of jobs. We also consider the nonclairvoyant setting where the size of a job is unknown upon its arrival and becomes known to the scheduler only when the job meets its service requirement. We consider the resource augmentation model, and give a {$ (1 + \varepsilon) $}-speed, {$ (1 + 1 / \varepsilon) $}-competitive online algorithm.", acknowledgement = ack-nhfb, articleno = "39", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "nonclairvoyant scheduling; online algorithms; response time; Scheduling", } @Article{Fakcharoenphol:2007:TRP, author = "Jittat Fakcharoenphol and Chris Harrelson and Satish Rao", title = "The $k$-traveling repairmen problem", journal = j-TALG, volume = "3", number = "4", pages = "40:1--40:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290677", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the $k$-traveling repairmen problem, also known as the minimum latency problem, to multiple repairmen. We give a polynomial-time $ 8.497 \alpha $-approximation algorithm for this generalization, where $ \alpha $ denotes the best achievable approximation factor for the problem of finding the least-cost rooted tree spanning $i$ vertices of a metric. For the latter problem, a $ (2 + \varepsilon) $-approximation is known. Our results can be compared with the best-known approximation algorithm using similar techniques for the case $ k = 1 $, which is $ 3.59 \alpha $. Moreover, recent work of Chaudry et al. [2003] shows how to remove the factor of $ \alpha $, thus improving all of these results by that factor. We are aware of no previous work on the approximability of the present problem. In addition, we give a simple proof of the $ 3.59 \alpha $-approximation result that can be more easily extended to the case of multiple repairmen, and may be of independent interest.", acknowledgement = ack-nhfb, articleno = "40", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Traveling salesman; vehicle routing", } @Article{Irani:2007:APS, author = "Sandy Irani and Sandeep Shukla and Rajesh Gupta", title = "Algorithms for power savings", journal = j-TALG, volume = "3", number = "4", pages = "41:1--41:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290678", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article examines two different mechanisms for saving power in battery-operated embedded systems. The first strategy is that the system can be placed in a sleep state if it is idle. However, a fixed amount of energy is required to bring the system back into an active state in which it can resume work. The second way in which power savings can be achieved is by varying the speed at which jobs are run. We utilize a power consumption curve {$ P(s) $} which indicates the power consumption level given a particular speed. We assume that {$ P(s) $} is convex, nondecreasing, and nonnegative for {$ s \geq 0 $}. The problem is to schedule arriving jobs in a way that minimizes total energy use and so that each job is completed after its release time and before its deadline. We assume that all jobs can be preempted and resumed at no cost. Although each problem has been considered separately, this is the first theoretical analysis of systems that can use both mechanisms. We give an offline algorithm that is within a factor of 2 of the optimal algorithm. We also give an online algorithm with a constant competitive ratio.", acknowledgement = ack-nhfb, articleno = "41", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "dynamic speed scaling; online algorithms; Power savings", } @Article{Alon:2007:GSE, author = "Noga Alon and Venkatesan Guruswami and Tali Kaufman and Madhu Sudan", title = "Guessing secrets efficiently via list decoding", journal = j-TALG, volume = "3", number = "4", pages = "42:1--42:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290679", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the guessing secrets problem defined by Chung et al. [2001]. This is a variant of the standard 20 questions game where the player has a set of $ k > 1 $ secrets from a universe of {$N$} possible secrets. The player is asked Boolean questions about the secret. For each question, the player picks one of the {$k$} secrets adversarially, and answers according to this secret.\par We present an explicit set of {$ O(\log N) $} questions together with an efficient (i.e., {$ {\rm poly}(\log N) $} time) algorithm to solve the guessing secrets problem for the case of 2 secrets. This answers the main algorithmic question left unanswered by Chung et al. [2001]. The main techniques we use are small {$ \epsilon $}-biased spaces and the notion of list decoding.\par We also establish bounds on the number of questions needed to solve the {$k$}-secrets game for {$ k > 2 $}, and discuss how list decoding can be used to get partial information about the secrets, specifically to find a small core of secrets that must intersect the actual set of $k$ secrets.", acknowledgement = ack-nhfb, articleno = "42", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "$\epsilon$-biased spaces; $k$-universal sets; 20 questions; decoding algorithms; error-correcting codes", } @Article{Raman:2007:SID, author = "Rajeev Raman and Venkatesh Raman and Srinivasa Rao Satti", title = "Succinct indexable dictionaries with applications to encoding $k$-ary trees, prefix sums and multisets", journal = j-TALG, volume = "3", number = "4", pages = "43:1--43:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290680", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the indexable dictionary problem, which consists of storing a set {$ S \subseteq \{ 0, \ldots, m - 1 \} $} for some integer {$m$} while supporting the operations of {$ \rank (x) $}, which returns the number of elements in {$S$} that are less than {$x$} if {$ x \in S $}, and {$ - 1 $} otherwise; and {$ \select (i) $}, which returns the {$i$} th smallest element in {$S$}. We give a data structure that supports both operations in {$ O(1) $} time on the RAM model and requires {$ B(n, m) + o(n) + O(\lg \lg m) $} bits to store a set of size {$n$}, where {$ B(n, m) = \lfloor \lg (m / n) \rfloor $} is the minimum number of bits required to store any {$n$}-element subset from a universe of size {$m$}. Previous dictionaries taking this space only supported (yes/no) membership queries in {$ O (1) $} time. In the cell probe model we can remove the {$ O (\lg \lg m) $} additive term in the space bound, answering a question raised by Fich and Miltersen [1995] and Pagh [2001].\par We present extensions and applications of our indexable dictionary data structure, including:\par --- an information-theoretically optimal representation of a {$k$}-ary cardinal tree that supports standard operations in constant time;\par --- a representation of a multiset of size {$n$} from {$ \{ 0, \ldots, m - 1 \} $} in {$ B(n, m + n) + o(n) $} bits that supports (appropriate generalizations of) rank and select operations in constant time; and {$ + O(\lg \lg m) $}\par --- a representation of a sequence of {$n$} nonnegative integers summing up to {$m$} in {$ B(n, m + n) + o(n) $} bits that supports prefix sum queries in constant time.", acknowledgement = ack-nhfb, articleno = "43", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Dictionaries; multisets; perfect hashing; prefix sums; sets; succinct data structures; tries", } @Article{Janson:2007:PFS, author = "Svante Janson and Wojciech Szpankowski", title = "Partial fillup and search time in {LC} tries", journal = j-TALG, volume = "3", number = "4", pages = "44:1--44:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290681", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Andersson and Nilsson introduced in 1993 a level-compressed trie (for short, LC trie) in which a full subtree of a node is compressed to a single node of degree being the size of the subtree. Recent experimental results indicated a ``dramatic improvement'' when full subtrees are replaced by ``partially filled subtrees.'' In this article, we provide a theoretical justification of these experimental results, showing, among others, a rather moderate improvement in search time over the original LC tries. For such an analysis, we assume that $n$ strings are generated independently by a binary memoryless source, with $p$ denoting the probability of emitting a ``1'' (and $ q = 1 - p $ ). We first prove that the so-called {$ \alpha $}-fillup level {$ F_n (\alpha) $} (i.e., the largest level in a trie with {$ \alpha $} fraction of nodes present at this level) is concentrated on two values with high probability: either {$ F_n(\alpha) = k_n $} or {$ F_n ({\alpha }) = k_n + 1 $}, where {$ k_n = \log 1 / \sqrt {pq} n - |l n(p / q)| / 2 l n 3 / 2 (1 \sqrt {pq}) {\Phi } - 1 (\alpha) \sqrt {\ln n} + O(1) $} is an integer and {$ \Phi (x) $} denotes the normal distribution function. This result directly yields the typical depth (search time) {$ D_n (\alpha) $} in the {$ \alpha $}-LC tries, namely, we show that with high probability {$ D_n(\alpha) \sim C_2 \log \log n $}, where {$ C_2 = 1 / | \log (1 - h / \log (1 / \sqrt {pq}))| $} for {$ p \neq q $} and {$ h = - p \log p - q \log q $} is the Shannon entropy rate. This should be compared with recently found typical depth in the original LC tries, which is {$ C_1 \log \log n $}, where {$ C_1 = 1 / | \log (1 - h) / \log (1 / \min \{ p, 1 - p \})| $}. In conclusion, we observe that {$ \alpha $} affects only the lower term of the {$ \alpha $}-fillup level {$ F_n(\alpha) $}, and the search time in {$ \alpha $}-LC tries is of the same order as in the original LC tries.", acknowledgement = ack-nhfb, articleno = "44", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Digital trees; level-compressed tries; partial fillup; Poissonization; probabilistic analysis; strings; trees", } @Article{Hershberger:2007:FSS, author = "John Hershberger and Matthew Maxel and Subhash Suri", title = "Finding the $k$ shortest simple paths: a new algorithm and its implementation", journal = j-TALG, volume = "3", number = "4", pages = "45:1--45:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290682", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We describe a new algorithm to enumerate the $k$ shortest simple (loopless) paths in a directed graph and report on its implementation. Our algorithm is based on a replacement paths algorithm proposed by Hershberger and Suri [2001], and can yield a factor {$ \Theta (n) $} improvement for this problem. But there is a caveat: The fast replacement paths subroutine is known to fail for some directed graphs. However, the failure is easily detected, and so our {$k$} shortest paths algorithm optimistically uses the fast subroutine, then switches to a slower but correct algorithm if a failure is detected. Thus, the algorithm achieves its {$ \Theta (n) $} speed advantage only when the optimism is justified. Our empirical results show that the replacement paths failure is a rare phenomenon, and the new algorithm outperforms the current best algorithms; the improvement can be substantial in large graphs. For instance, on GIS map data with about 5,000 nodes and 12,000 edges, our algorithm is 4--8 times faster. In synthetic graphs modeling wireless ad hoc networks, our algorithm is about 20 times faster.", acknowledgement = ack-nhfb, articleno = "45", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "directed paths; Loop-free paths; path equivalence class; replacement paths", } @Article{Chekuri:2007:EDP, author = "Chandra Chekuri and Sanjeev Khanna", title = "Edge-disjoint paths revisited", journal = j-TALG, volume = "3", number = "4", pages = "46:1--46:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290683", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The approximability of the maximum edge-disjoint paths problem (EDP) in directed graphs was seemingly settled by an {$ \Omega (m^{1 / 2} - \epsilon) $}-hardness result of Guruswami et al. [2003], and an {$ O(\sqrt {m}) $} approximation achievable via a natural multicommodity-flow-based LP relaxation as well as a greedy algorithm. Here {$m$} is the number of edges in the graph. We observe that the {$ \Omega (m^{1 / 2} - {\epsilon }) $}-hardness of approximation applies to sparse graphs, and hence when expressed as a function of {$n$}, that is, the number of vertices, only an {$ \Omega (n^{1 / 2} - \epsilon) $}-hardness follows. On the other hand, {$ O(\sqrt {m}) $}-approximation algorithms do not guarantee a sublinear (in terms of {$n$} ) approximation algorithm for dense graphs. We note that a similar gap exists in the known results on the integrality gap of the flow-based LP relaxation: an {$ \Omega (\sqrt {n}) $} lower bound and {$ O(\sqrt {m}) $} upper bound. Motivated by this discrepancy in the upper and lower bounds, we study algorithms for EDP in directed and undirected graphs and obtain improved approximation ratios. We show that the greedy algorithm has an approximation ratio of {$ O(\min (n^{2 / 3}, \sqrt {m})) $} in undirected graphs and a ratio of {$ O(\min (n^{4 / 5}, \sqrt {m})) $} in directed graphs. For acyclic graphs we give an {$ O(\sqrt {n} \ln n) $} approximation via LP rounding. These are the first sublinear approximation ratios for EDP. The results also extend to EDP with weights and to the uniform-capacity unsplittable flow problem (UCUFP).", acknowledgement = ack-nhfb, articleno = "46", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithm; Edge-disjoint paths; greedy algorithm; multicommodity flow relaxation", } @Article{Cheriyan:2007:PED, author = "Joseph Cheriyan and Mohammad R. Salavatipour", title = "Packing element-disjoint {Steiner} trees", journal = j-TALG, volume = "3", number = "4", pages = "47:1--47:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290684", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given an undirected graph {$ G(V, E) $} with terminal set {$ T \subseteq V $}, the problem of packing element-disjoint Steiner trees is to find the maximum number of Steiner trees that are disjoint on the nonterminal nodes and on the edges. The problem is known to be NP-hard to approximate within a factor of {$ \Omega (\log n) $}, where {$n$} denotes {$ |V| $}. We present a randomized {$ O(\log n) $}-approximation algorithm for this problem, thus matching the hardness lower bound. Moreover, we show a tight upper bound of {$ O(\log n) $} on the integrality ratio of a natural linear programming relaxation.", acknowledgement = ack-nhfb, articleno = "47", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithms; element-disjoint; hardness of approximation; Packing; Steiner trees", } @Article{Krivelevich:2007:AAH, author = "Michael Krivelevich and Zeev Nutov and Mohammad R. Salavatipour and Jacques Verstraete Yuster and Raphael Yuster", title = "Approximation algorithms and hardness results for cycle packing problems", journal = j-TALG, volume = "3", number = "4", pages = "48:1--48:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290685", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The cycle packing number {$ \nu e(G) $} of a graph {$G$} is the maximum number of pairwise edge-disjoint cycles in {$G$}. Computing {$ \nu e(G) $} is an NP-hard problem. We present approximation algorithms for computing {$ \nu e (G) $} in both undirected and directed graphs. In the undirected case we analyze a variant of the modified greedy algorithm suggested by Caprara et al. [2003] and show that it has approximation ratio {$ \Theta (\sqrt {\log n}) $}, where {$ n = |V(G)| $}. This improves upon the previous {$ O(\log n) $} upper bound for the approximation ratio of this algorithm. In the directed case we present a {$ \sqrt {n} $}-approximation algorithm. Finally, we give an {$ O(n^{2 / 3}) $}-approximation algorithm for the problem of finding a maximum number of edge-disjoint cycles that intersect a specified subset {$S$} of vertices. We also study generalizations of these problems. Our approximation ratios are the currently best-known ones and, in addition, provide upper bounds on the integrality gap of standard LP-relaxations of these problems. In addition, we give lower bounds for the integrality gap and approximability of {$ \nu e(G) $} in directed graphs. Specifically, we prove a lower bound of {$ \Omega (\log n / \log \log n) $} for the integrality gap of edge-disjoint cycle packing. We also show that it is quasi-NP-hard to approximate {$ \nu e(G) $} within a factor of {$ O(\log 1 - \varepsilon n) $} for any constant {$ \varepsilon > 0 $}. This improves upon the previously known APX-hardness result for this problem.", acknowledgement = ack-nhfb, articleno = "48", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithms; Cycle packing; edge-disjoint; hardness of approximation; integrality gap", } @Article{Albers:2007:EEA, author = "Susanne Albers and Hiroshi Fujiwara", title = "Energy-efficient algorithms for flow time minimization", journal = j-TALG, volume = "3", number = "4", pages = "49:1--49:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290686", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study scheduling problems in battery-operated computing devices, aiming at schedules with low total energy consumption. While most of the previous work has focused on finding feasible schedules in deadline-based settings, in this article we are interested in schedules that guarantee good response times. More specifically, our goal is to schedule a sequence of jobs on a variable-speed processor so as to minimize the total cost consisting of the energy consumption and the total flow time of all jobs.\par We first show that when the amount of work, for any job, may take an arbitrary value, then no online algorithm can achieve a constant competitive ratio. Therefore, most of the article is concerned with unit-size jobs. We devise a deterministic constant competitive online algorithm and show that the offline problem can be solved in polynomial time.", acknowledgement = ack-nhfb, articleno = "49", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "competitive analysis; dynamic programming; flow time; offline algorithms; online algorithms; Variable-speed processor", } @Article{Chrobak:2007:IOA, author = "Marek Chrobak and Wojciech Jawor and Ji{\v{r}}{\'\i} Sgall and Tom{\'a}{\v{s}} Tich{\'y}", title = "Improved online algorithms for buffer management in {QoS} switches", journal = j-TALG, volume = "3", number = "4", pages = "50:1--50:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290687", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the following buffer management problem arising in QoS networks: Packets with specified weights and deadlines arrive at a network switch and need to be forwarded so that the total weight of forwarded packets is maximized. Packets not forwarded before their deadlines are lost. The main result of the article is an online $ 64 / 33 \approx 1.939 $-competitive algorithm, the first deterministic algorithm for this problem with competitive ratio below 2. For the 2-uniform case we give an algorithm with ratio $ \approx 1.377 $ and a matching lower bound.", acknowledgement = ack-nhfb, articleno = "50", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Online algorithms; scheduling", } @Article{Hajiaghayi:2007:ORN, author = "Mohammad Taghi Hajiaghayi and Robert D. Kleinberg and Harald R{\"a}cke and Tom Leighton", title = "Oblivious routing on node-capacitated and directed graphs", journal = j-TALG, volume = "3", number = "4", pages = "51:1--51:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290688", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Oblivious routing algorithms for general undirected networks were introduced by R{\"a}cke [2002], and this work has led to many subsequent improvements and applications. Comparatively little is known about oblivious routing in general directed networks, or even in undirected networks with node capacities.\par We present the first nontrivial upper bounds for both these cases, providing algorithms for $k$-commodity oblivious routing problems with competitive ratio {$ O(\sqrt {k \log (n)}) $} for undirected node-capacitated graphs and {$ O(\sqrt {k_n} 1 / 4 \log (n)) $} for directed graphs. In the special case that all commodities have a common source or sink, our upper bound becomes {$ O(\sqrt {n} \log (n)) $} in both cases, matching the lower bound up to a factor of {$ \log (n) $}. The lower bound (which first appeared in Azar et al. [2003]) is obtained on a graph with very high degree. We show that, in fact, the degree of a graph is a crucial parameter for node-capacitated oblivious routing in undirected graphs, by providing an {$ O(\Delta \polylog (n)) $}-competitive oblivious routing scheme for graphs of degree {$ \Delta $}. For the directed case, however, we show that the lower bound of {$ \Omega (\sqrt {n}) $} still holds in low-degree graphs.\par Finally, we settle an open question about routing problems in which all commodities share a common source or sink. We show that even in this simplified scenario there are networks in which no oblivious routing algorithm can achieve a competitive ratio better than {$ \Omega (\log n) $}.", acknowledgement = ack-nhfb, articleno = "51", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "communication networks; directed graphs; node-capacitated graphs; Oblivious routing", } @Article{Auletta:2007:RSU, author = "Vincenzo Auletta and Roberto {De Prisco} and Paolo Penna and Giuseppe Persiano", title = "Routing selfish unsplittable traffic", journal = j-TALG, volume = "3", number = "4", pages = "52:1--52:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290689", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider general resource assignment games involving selfish users/agents in which users compete for resources and try to be assigned to those which maximize their own benefits (e.g., try to route their traffic through links which minimize the latency of their own traffic). We propose and study a mechanism design approach in which an allocation mechanism assigns users to resources and charges the users for using the resources so as to induce each user to truthfully report a private piece of information he/she holds (e.g., how much traffic he/she needs to transmit). This information is crucial for computing optimal (or close to optimal) allocations and an agent could misreport his/her information to induce the underlying allocation algorithm to output a solution which he/she likes more (e.g., which assigns better resources to him/her).\par For our resource allocation problems, we give an algorithmic characterization of the solutions for which truth-telling is a Nash equilibrium. A natural application of these results is to a scheduling/routing problem which is the mechanism design counterpart of the selfish routing game of Koutsoupias and Papadimitriou [1999]: Each selfish user wants to route a piece of unsplittable traffic using one of $m$ links of different speeds so as to minimize his/her own latency. Our mechanism design counterpart can be seen as the problem of scheduling selfish jobs on parallel related machines and is the dual of the problem of scheduling (unselfish) jobs on parallel selfish machines studied by Archer and Tardos [2001].\par Koutsoupias and Papadimitriou studied an ``anarchic'' scenario in which each user chooses his/her own link, and this may produce Nash equilibria of cost {$ \Omega (\log m / \log \log m) $} times the optimum. Our mechanism design counterpart is a possible way of reducing the effect of selfish behavior via suitable incentives to the agents (i.e., taxes for using the links). We indeed show that in the resulting game, it is possible to guarantee an approximation factor of 8 for any number of links/machines (this solution also works for online settings). However, it remains impossible to guarantee arbitrarily good approximate solutions, even for 2 links/machines and even if the allocation algorithm is allowed superpolynomial time. This result shows that our scheduling problem with selfish jobs is more difficult than the scheduling problem with selfish machines by Archer and Tardos (which admits exact solutions).\par We also study some generalizations of this basic problem.", acknowledgement = ack-nhfb, articleno = "52", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Algorithmic mechanism design; Nash equilibrium; scheduling; selfish routing", } @Article{Ruzic:2008:UDD, author = "Milan Ru{\v{z}}i{\'c}", title = "Uniform deterministic dictionaries", journal = j-TALG, volume = "4", number = "1", pages = "1:1--1:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328912", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a new analysis of the well-known family of multiplicative hash functions, and improved deterministic algorithms for selecting ``good'' hash functions. The main motivation is realization of deterministic dictionaries with fast lookups and reasonably fast updates. The model of computation is the Word RAM, and it is assumed that the machine word-size matches the size of keys in bits. Many of the modern solutions to the dictionary problem are weakly nonuniform, that is, they require a number of constants to be computed at ``compile time'' for the stated time bounds to hold. The currently fastest deterministic dictionary uses constants not known to be computable in polynomial time. In contrast, our dictionaries do not require any special constants or instructions, and running times are independent of word (and key) length. Our family of dynamic dictionaries achieves a performance of the following type: lookups in time {$ O(t) $} and updates in amortized time {$ O(n^{1 / t}) $}, for an appropriate parameter function {$t$}. Update procedures require division, whereas searching uses multiplication only.", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Deterministic algorithms; perfect hashing", } @Article{Franceschini:2008:NSB, author = "Gianni Franceschini and Roberto Grossi", title = "No sorting? better searching!", journal = j-TALG, volume = "4", number = "1", pages = "2:1--2:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328913", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Questions about order versus disorder in systems and models have been fascinating scientists over the years. In computer science, order is intimately related to sorting, commonly meant as the task of arranging keys in increasing or decreasing order with respect to an underlying total order relation. The sorted organization is amenable for searching a set of $n$ keys, since each search requires {$ \Theta (\log n) $} comparisons in the worst case, which is optimal if the cost of a single comparison can be considered a constant. Nevertheless, we prove that disorder implicitly provides more information than order does. For the general case of searching an array of multidimensional keys whose comparison cost is proportional to their length (and hence which cannot be considered a constant), we demonstrate that ``suitable'' disorder gives better bounds than those derivable by using the natural lexicographic order.\par We start from previous work done by Andersson et al. [2001], who proved that {$ \Theta (k \log \log n / \log \log (4 + k \log \log n / \log n) + k + \log n) $} character comparisons (or probes) comprise the tight complexity for searching a plain sorted array of {$n$} keys, each of length {$k$}, arranged in lexicographic order. We describe a novel permutation of the {$n$} keys that is different from the sorted order. When keys are kept ``unsorted'' in the array according to this permutation, the complexity of searching drops to {$ \Theta (k + \log n) $} character comparisons (or probes) in the worst case, which is optimal among all possible permutations, up to a constant factor. Consequently, disorder carries more information than does order; this fact was not observable before, since the latter two bounds are {$ \Theta (\log n) $} when {$ k = O(1) $}. More implications are discussed in the article, including searching in the bit-probe model.", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Implicit data structures; in-place algorithms; searching; sorting", } @Article{Kaplan:2008:THT, author = "Haim Kaplan and Robert Endre Tarjan", title = "Thin heaps, thick heaps", journal = j-TALG, volume = "4", number = "1", pages = "3:1--3:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328914", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The Fibonacci heap was devised to provide an especially efficient implementation of Dijkstra's shortest path algorithm. Although asymptotically efficient, it is not as fast in practice as other heap implementations. Expanding on ideas of H{\o}yer [1995], we describe three heap implementations (two versions of thin heaps and one of thick heaps) that have the same amortized efficiency as Fibonacci heaps, but need less space and promise better practical performance. As part of our development, we fill in a gap in H{\o}yer's analysis.", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "binomial queue; Data structure; decrease key operation; Fibonacci heap; heap; melding; priority queue; thick heap; thin heap", } @Article{Barbay:2008:ARA, author = "J{\'e}r{\'e}my Barbay and Claire Kenyon", title = "Alternation and redundancy analysis of the intersection problem", journal = j-TALG, volume = "4", number = "1", pages = "4:1--4:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328915", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The intersection of sorted arrays problem has applications in search engines such as Google. Previous work has proposed and compared deterministic algorithms for this problem, in an adaptive analysis based on the encoding size of a certificate of the result (cost analysis). We define the alternation analysis, based on the nondeterministic complexity of an instance. In this analysis we prove that there is a deterministic algorithm asymptotically performing as well as any randomized algorithm in the comparison model. We define the redundancy analysis, based on a measure of the internal redundancy of the instance. In this analysis we prove that any algorithm optimal in the redundancy analysis is optimal in the alternation analysis, but that there is a randomized algorithm which performs strictly better than any deterministic algorithm in the comparison model. Finally, we describe how these results can be extended beyond the comparison model.", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Adaptive analysis; alternation analysis; intersection; intersection of sorted arrays; randomized algorithm; redundancy analysis", } @Article{Pettie:2008:RMS, author = "Seth Pettie and Vijaya Ramachandran", title = "Randomized minimum spanning tree algorithms using exponentially fewer random bits", journal = j-TALG, volume = "4", number = "1", pages = "5:1--5:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328916", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "For many fundamental problems there exist randomized algorithms that are asymptotically optimal and are superior to the best-known deterministic algorithm. Among these are the minimum spanning tree (MST) problem, the MST sensitivity analysis problem, the parallel connected components and parallel minimum spanning tree problems, and the local sorting and set maxima problems. (For the first two problems there are provably optimal deterministic algorithms with unknown, and possibly superlinear, running times.) One downside of the randomized methods for solving these problems is that they use a number of random bits linear in the size of input. In this article we develop some general methods for reducing exponentially the consumption of random bits in comparison-based algorithms. In some cases we are able to reduce the number of random bits from linear to nearly constant, without affecting the expected running time.\par Most of our results are obtained by adjusting or reorganizing existing randomized algorithms to work well with a pairwise or {$ O(1) $}-wise independent sampler. The prominent exception, and the main focus of this article, is a linear-time randomized minimum spanning tree algorithm that is not derived from the well-known Karger-Klein-Tarjan algorithm. In many ways it resembles more closely the deterministic minimum spanning tree algorithms based on soft heaps. Further, using our algorithm as a guide, we present a unified view of the existing ``nongreedy'' minimum spanning tree algorithms. Concepts from the Karger-Klein-Tarjan algorithm, such as F-lightness, MST verification, and sampled graphs, are related to the concepts of edge corruption, subgraph contractibility, and soft heaps, which are the basis of the deterministic MST algorithms of Chazelle and Pettie-Ramachandran.", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Graph algorithms; minimum spanning trees; random sampling", } @Article{Roditty:2008:FSF, author = "Liam Roditty", title = "A faster and simpler fully dynamic transitive closure", journal = j-TALG, volume = "4", number = "1", pages = "6:1--6:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328917", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We obtain a new fully dynamic algorithm for maintaining the transitive closure of a directed graph. Our algorithm maintains the transitive closure matrix in a total running time of {$ O(m n + ({\rm ins} + {\rm del}) {\cdot } n^2) $}, where ins(del) is the number of insert (delete) operations performed. Here {$n$} is the number of vertices in the graph and {$m$} is the initial number of edges in the graph. Obviously, reachability queries can be answered in constant time. The algorithm uses only {$ O(n^2) $} time which is essentially optimal for maintaining the transitive closure matrix. Our algorithm can also support path queries. If {$v$} is reachable from {$u$}, the algorithm can produce a path from {$u$} to $v$ in time proportional to the length of the path. The best previously known algorithm for the problem is due to Demetrescu and Italiano [2000]. Their algorithm has a total running time of {$ O(n^3 + ({\rm ins} + {\rm del}) {\cdot } n^2) $}. The query time is also constant. In addition, we also present a simple algorithm for directed acyclic graphs (DAGs) with a total running time of {$ O(m n + {\rm ins} {\cdot } n^2 + {\rm del}) $}. Our algorithms are obtained by combining some new ideas with techniques of Italiano [1986, 1988], King [1999], King and Thorup [2001] and Frigioni et al. [2001]. We also note that our algorithms are extremely simple and can be easily implemented.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "directed graph; Dynamic graph algorithms; reachability", } @Article{Gabow:2008:FLD, author = "Harold N. Gabow and Shuxin Nie", title = "Finding a long directed cycle", journal = j-TALG, volume = "4", number = "1", pages = "7:1--7:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328918", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Consider a digraph with $n$ vertices. For any fixed value $k$, we present linear- and almost-linear-time algorithms to find a cycle of length $ \geq k $, if one exists. We also find a cycle that has length $ \geq \log n / \log \log n $ in polynomial time, if one exists. Under an appropriate complexity assumption it is known to be impossible to improve this guarantee by more than a $ \log \log n $ factor. Our approach is based on depth-first search.", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; circumference; cycles; Hamiltonian cycles; long cycles", } @Article{Buchsbaum:2008:RLC, author = "Adam L. Buchsbaum and Emden R. Gansner and Cecilia M. Procopiuc and Suresh Venkatasubramanian", title = "Rectangular layouts and contact graphs", journal = j-TALG, volume = "4", number = "1", pages = "8:1--8:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328919", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Contact graphs of isothetic rectangles unify many concepts from applications including VLSI and architectural design, computational geometry, and GIS. Minimizing the area of their corresponding rectangular layouts is a key problem. We study the area-optimization problem and show that it is NP-hard to find a minimum-area rectangular layout of a given contact graph. We present {$ O(n) $}-time algorithms that construct {$ O(n^2) $}-area rectangular layouts for general contact graphs and {$ O(n \log n) $}-area rectangular layouts for trees. (For trees, this is an {$ O(\log n) $}-approximation algorithm.) We also present an infinite family of graphs (respectively, trees) that require {$ \Omega (n^2) $} (respectively, {$ \Omega (n \log n) $}) area.\par We derive these results by presenting a new characterization of graphs that admit rectangular layouts, using the related concept of rectangular duals. A corollary to our results relates the class of graphs that admit rectangular layouts to rectangle-of-influence drawings.", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Contact graphs; rectangular duals; rectangular layouts", } @Article{Arge:2008:PRT, author = "Lars Arge and Mark {De Berg} and Herman Haverkort and Ke Yi", title = "The priority {R}-tree: a practically efficient and worst-case optimal {R}-tree", journal = j-TALG, volume = "4", number = "1", pages = "9:1--9:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328920", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present the priority R-tree, or PR-tree, which is the first R-tree variant that always answers a window query using {$ O((N / B) 1 - 1 / d + T / B) $} I/Os, where {$N$} is the number of {$d$}-dimensional (hyper-) rectangles stored in the R-tree, {$B$} is the disk block size, and {$T$} is the output size. This is provably asymptotically optimal and significantly better than other R-tree variants, where a query may visit all {$ N / B $} leaves in the tree even when {$ T = 0 $}. We also present an extensive experimental study of the practical performance of the PR-tree using both real-life and synthetic data. This study shows that the PR-tree performs similarly to the best-known R-tree variants on real-life and relatively nicely distributed data, but outperforms them significantly on more extreme data.", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "R-trees", } @Article{Gudmundsson:2008:ADO, author = "Joachim Gudmundsson and Christos Levcopoulos and Giri Narasimhan and Michiel Smid", title = "Approximate distance oracles for geometric spanners", journal = j-TALG, volume = "4", number = "1", pages = "10:1--10:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328921", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given an arbitrary real constant $ \varepsilon > 0 $, and a geometric graph {$G$} in {$d$}-dimensional Euclidean space with {$n$} points, {$ O(n) $} edges, and constant dilation, our main result is a data structure that answers {$ (1 + \varepsilon) $}-approximate shortest-path-length queries in constant time. The data structure can be constructed in {$ O(n \log n) $} time using {$ O(n \log n) $} space. This represents the first data structure that answers {$ (1 + \varepsilon) $}-approximate shortest-path queries in constant time, and hence functions as an approximate distance oracle. The data structure is also applied to several other problems. In particular, we also show that approximate shortest-path queries between vertices in a planar polygonal domain with ``rounded'' obstacles can be answered in constant time. Other applications include query versions of closest-pair problems, and the efficient computation of the approximate dilations of geometric graphs. Finally, we show how to extend the main result to answer {$ (1 + \varepsilon) $}-approximate shortest-path-length queries in constant time for geometric spanner graphs with {$ m = \omega (n) $} edges. The resulting data structure can be constructed in {$ O(m + n \log n) $} time using {$ O(n \log n) $} space.", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithm; computational geometry; geometric graphs; Shortest paths; spanners", } @Article{Gandhi:2008:IBS, author = "Rajiv Gandhi and Magn{\'u}s M. Halld{\'o}rsson and Guy Kortsarz and Hadas Shachnai", title = "Improved bounds for scheduling conflicting jobs with minsum criteria", journal = j-TALG, volume = "4", number = "1", pages = "11:1--11:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328922", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider a general class of scheduling problems where a set of conflicting jobs needs to be scheduled (preemptively or nonpreemptively) on a set of machines so as to minimize the weighted sum of completion times. The conflicts among jobs are formed as an arbitrary conflict graph.\par Building on the framework of Queyranne and Sviridenko [2002b], we present a general technique for reducing the weighted sum of completion-times problem to the classical makespan minimization problem. Using this technique, we improve the best-known results for scheduling conflicting jobs with the min-sum objective, on several fundamental classes of graphs, including line graphs, $ (k + 1) $-claw-free graphs, and perfect graphs. In particular, we obtain the first constant-factor approximation ratio for nonpreemptive scheduling on interval graphs. We also improve the results of Kim [2003] for scheduling jobs on line graphs and for resource-constrained scheduling.", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; coloring; linear programming; LP rounding; scheduling; sum multicoloring", } @Article{Guerraoui:2008:CMA, author = "Rachid Guerraoui and Ron R. Levy and Bastian Pochon and Jim Pugh", title = "The collective memory of amnesic processes", journal = j-TALG, volume = "4", number = "1", pages = "12:1--12:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328923", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article considers the problem of robustly emulating a shared atomic memory over a distributed message-passing system where processes can fail by crashing and possibly recover. We revisit the notion of atomicity in the crash-recovery context and introduce a generic algorithm that emulates an atomic memory. The algorithm is instantiated for various settings according to whether processes have access to local stable storage, and whether, in every execution of the algorithm, a sufficient number of processes are assumed not to crash. We establish the optimality of specific instances of our algorithm in terms of resilience, log complexity (number of stable storage accesses needed in every read or write operation), as well as time complexity (number of communication steps needed in every read or write operation). The article also discusses the impact of considering a multiwriter versus a single-writer memory, as well as the impact of weakening the consistency of the memory by providing safe or regular semantics instead of atomicity.", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "\log complexity; Atomic registers; crash recovery; shared-memory emulation", } @Article{Karakostas:2008:FAS, author = "George Karakostas", title = "Faster approximation schemes for fractional multicommodity flow problems", journal = j-TALG, volume = "4", number = "1", pages = "13:1--13:17", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328924", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present fully polynomial approximation schemes for concurrent multicommodity flow problems that run in time of the minimum possible dependencies on the number of commodities $k$. We show that by modifying the algorithms by Garg and K{\"o}nemann [1998] and Fleischer [2000], we can reduce their running time on a graph with $n$ vertices and $m$ edges from {$ \tilde {O}(\varepsilon^{ - 2}(m^2 + k m)) $} to {$ \tilde {O}({\varepsilon^{ - 2m}}^2) $} for an {\em implicit\/} representation of the output, or {$ \tilde {O}(\varepsilon^{ - 2}(m^2 + k n)) $} for an {\em explicit\/} representation, where {$ \tilde {O}(f) $} denotes a quantity that is {$ O(f \log^{O(1)} m)$}. The implicit representation consists of a set of trees rooted at sources (there can be more than one tree per source), and with sinks as their leaves, together with flow values for the flow directed from the source to the sinks in a particular tree. Given this implicit representation, the approximate value of the concurrent flow is known, but if we want the explicit flow per commodity per edge, we would have to combine all these trees together, and the cost of doing so may be prohibitive. In case we want to calculate explicitly the solution flow, we modify our schemes so that they run in time polylogarithmic in {$ n k $} ({$n$} is the number of nodes in the network). This is within a polylogarithmic factor of the trivial lower bound of time {$ \Omega (n k) $} needed to explicitly write down a multicommodity flow of {$k$} commodities in a network of {$n$} nodes. Therefore our schemes are within a polylogarithmic factor of the minimum possible dependencies of the running time on the number of commodities {$k$}.", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "fully-polynomial time approximation schemes; Multicommodity flows", } @Article{Lemire:2008:HBO, author = "Daniel Lemire and Owen Kaser", title = "Hierarchical bin buffering: {Online} local moments for dynamic external memory arrays", journal = j-TALG, volume = "4", number = "1", pages = "14:1--14:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328925", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "For a massive I/O array of size $n$, we want to compute the first {$N$} local moments, for some constant {$N$}. Our simpler algorithms partition the array into consecutive ranges called bins, and apply not only to local-moment queries, but also to algebraic queries. With {$N$} buffers of size {$ \sqrt {n} $}, time complexity drops to {$ O(\sqrt {n}) $}. A more sophisticated approach uses hierarchical buffering and has a logarithmic time complexity ({$ O(b \log b n) $}), when using {$N$} hierarchical buffers of size {$ n / b $}. Using overlapped bin buffering, we show that only one buffer is needed, as with wavelet-based algorithms, but using much less storage.", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "hierarchical buffers; polynomial fitting; statistical queries; Very large arrays", } @Article{Anshelevich:2008:PDU, author = "Elliot Anshelevich and Lisa Zhang", title = "Path decomposition under a new cost measure with applications to optical network design", journal = j-TALG, volume = "4", number = "1", pages = "15:1--15:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328926", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce a problem directly inspired by its application to DWDM (dense wavelength division multiplexing) network design. We are given a set of demands to be carried over a network. Our goal is to choose a route for each demand and to decompose the network into a collection of edge-disjoint simple paths. These paths are called optical line systems. The cost of routing one unit of demand is the number of line systems with which the demand route overlaps; our design objective is to minimize the total cost over all demands. This cost metric is motivated by the need to minimize O-E-O(optical-electrical-optical) conversions in optical transmission.\par For given line systems, it is easy to find the optimal demand routes. On the other hand, for given demand routes designing the optimal line systems can be NP-hard. We first present a 2-approximation for general network topologies. As optical networks often have low node degrees, we offer an algorithm that finds the optimal solution for the special case in which the node degree is at most 3. Our solution is based on a local greedy approach.\par If neither demand routes nor line systems are fixed, the situation becomes much harder. Even for a restricted scenario on a 3-regular Hamiltonian network, no efficient algorithm can guarantee a constant approximation better than 2. For general topologies, we offer a simple algorithm with an {$ O(\log K) $}- and an {$ O(\log n) $}-approximation, where {$K$} is the number of demands and {$n$} the number of nodes. This approximation ratio is almost tight. For rings, a common special topology, we offer a more complex 3/2-approximation algorithm.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithms; Optical network design; path decomposition", } @Article{Buchsbaum:2008:GE, author = "Adam L. Buchsbaum", title = "Guest editorial", journal = j-TALG, volume = "4", number = "2", pages = "16:1--16:??", month = may, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1361192.1361193", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:51 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Blandford:2008:CDV, author = "Daniel K. Blandford and Guy E. Blelloch", title = "Compact dictionaries for variable-length keys and data with applications", journal = j-TALG, volume = "4", number = "2", pages = "17:1--17:??", month = may, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1361192.1361194", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:51 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problem of maintaining a dynamic dictionary {$T$} of keys and associated data for which both the keys and data are bit strings that can vary in length from zero up to the length {$w$} of a machine word. We present a data structure for this variable-bit-length dictionary problem that supports constant time lookup and expected amortized constant-time insertion and deletion. It uses {$ O(m + 3 n - n \log 2 n) $} bits, where {$n$} is the number of elements in {$T$}, and {$m$} is the total number of bits across all strings in {$T$} (keys and data). Our dictionary uses an array {$ A[1 \ldots n] $} in which locations store variable-bit-length strings. We present a data structure for this variable-bit-length array problem that supports worst-case constant-time lookups and updates and uses {$ O(m + n) $} bits, where {$m$} is the total number of bits across all strings stored in {$A$}.\par The motivation for these structures is to support applications for which it is helpful to efficiently store short varying-length bit strings. We present several applications, including representations for semidynamic graphs, order queries on integers sets, cardinal trees with varying cardinality, and simplicial meshes of {$d$} dimensions. These results either generalize or simplify previous results.", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Compression", } @Article{Kolluri:2008:PGM, author = "Ravikrishna Kolluri", title = "Provably good moving least squares", journal = j-TALG, volume = "4", number = "2", pages = "18:1--18:??", month = may, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1361192.1361195", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:51 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We analyze a moving least squares (MLS) interpolation scheme for reconstructing a surface from point cloud data. The input is a sufficiently dense set of sample points that lie near a closed surface F with approximate surface normals. The output is a reconstructed surface passing near the sample points. For each sample point $s$ in the input, we define a linear point function that represents the local shape of the surface near $s$. These point functions are combined by a weighted average, yielding a three-dimensional function {$I$}. The reconstructed surface is implicitly defined as the zero set of {$I$}.\par We prove that the function {$I$} is a good approximation to the signed distance function of the sampled surface {$F$} and that the reconstructed surface is geometrically close to and isotopic to {$F$}. Our sampling requirements are derived from the local feature size function used in Delaunay-based surface reconstruction algorithms. Our analysis can handle noisy data provided the amount of noise in the input dataset is small compared to the feature size of {$F$}.", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "implicit surfaces; interpolation; Reconstruction", } @Article{Fusy:2008:DOT, author = "{\'E}ric Fusy and Gilles Schaeffer and Dominique Poulalhon", title = "Dissections, orientations, and trees with applications to optimal mesh encoding and random sampling", journal = j-TALG, volume = "4", number = "2", pages = "19:1--19:??", month = may, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1361192.1361196", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:51 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a bijection between some quadrangular dissections of an hexagon and unrooted binary trees with interesting consequences for enumeration, mesh compression, and graph sampling. Our bijection yields an efficient uniform random sampler for 3-connected planar graphs, which turns out to be determinant for the quadratic complexity of the current best-known uniform random sampler for labelled planar graphs. It also provides an encoding for the set {$ P(n) $} of {$n$}-edge 3-connected planar graphs that matches the entropy bound {$ 1 / n \log 2 | P(n)| = 2 + o (1) $} bits per edge (bpe). This solves a theoretical problem recently raised in mesh compression as these graphs abstract the combinatorial part of meshes with spherical topology. We also achieve the optimal parametric rate {$ 1 / n \log 2 | P(n, i, j)| $} bpe for graphs of {$ P(n) $} with {$i$} vertices and {$j$} faces, matching in particular the optimal rate for triangulations. Our encoding relies on a linear time algorithm to compute an orientation associated with the minimal Schnyder wood of a 3-connected planar map. This algorithm is of independent interest, and it is, for instance, a key ingredient in a recent straight line drawing algorithm for 3-connected planar graphs.", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Bijection; coding; counting; random generation", } @Article{VeghVegh:2008:PDA, author = "L{\'a}szl{\'o} A. V{\'e}ghV{\'e}gh and Andr{\'a}s A. Bencz{\'u}r", title = "Primal-dual approach for directed vertex connectivity augmentation and generalizations", journal = j-TALG, volume = "4", number = "2", pages = "20:1--20:??", month = may, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1361192.1361197", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:51 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In their seminal paper, Frank and Jord{\'a}n [1995] show that a large class of optimization problems, including certain directed graph augmentation, fall into the class of covering supermodular functions over pairs of sets. They also give an algorithm for such problems, however, it relies on the ellipsoid method. Prior to our result, combinatorial algorithms existed only for the 0--1 valued problem. Our key result is a combinatorial algorithm for the general problem that includes directed vertex or S-T connectivity augmentation. The algorithm is based on Bencz{\'u}r's previous algorithm for the 0--1 valued case [Bencz{\'u}r 2003].\par Our algorithm uses a primal-dual scheme for finding covers of partially ordered sets that satisfy natural abstract properties as in Frank and Jord{\'a}n. For an initial (possibly greedy) cover, the algorithm searches for witnesses for the necessity of each element in the cover. If no two (weighted) witnesses have a common cover, the solution is optimal. As long as this is not the case, the witnesses are gradually exchanged for smaller ones. Each witness change defines an appropriate change in the solution; these changes are finally unwound in a shortest-path manner to obtain a solution of size one less.", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "combinatorial algorithm; Vertex connectivity augmentation", } @Article{Sanders:2008:AAS, author = "Peter Sanders and David Steurer", title = "An asymptotic approximation scheme for multigraph edge coloring", journal = j-TALG, volume = "4", number = "2", pages = "21:1--21:??", month = may, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1361192.1361198", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:51 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The edge coloring problem considers the assignment of colors from a minimum number of colors to edges of a graph such that no two edges with the same color are incident to the same node. We give polynomial time algorithms for approximate edge coloring of multigraphs, that is, parallel edges are allowed. The best previous algorithms achieve a fixed constant approximation factor plus a small additive offset. One of our algorithms achieves solution quality $ {\rm opt} + \sqrt {9 {\rm opt} / 2} $ and has execution time polynomial in the number of nodes and the logarithm of the maximum edge multiplicity.", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "chromatic index; data migration; Edge coloring; multigraphs", } @Article{Chawla:2008:ENT, author = "Shuchi Chawla and Anupam Gupta and Harald R{\"a}cke", title = "Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut", journal = j-TALG, volume = "4", number = "2", pages = "22:1--22:??", month = may, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1361192.1361199", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:51 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we study metrics of negative type, which are metrics {$ (V, d) $} such that {$ \sqrt {d} $} is an Euclidean metric; these metrics are thus also known as {$ \ell_2 $}-squared metrics. We show how to embed {$n$}-point negative-type metrics into Euclidean space $ \ell_2 $ with distortion {$ D = O(\log 3 / 4 n) $}. This embedding result, in turn, implies an {$ O(\log 3 / 4 k) $}-approximation algorithm for the Sparsest Cut problem with nonuniform demands. Another corollary we obtain is that {$n$}-point subsets of {$ \ell_1 $} embed into {$ \ell_2 $} with distortion {$ O(\log 3 / 4 n) $}.", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithm; embedding; metrics; negative-type metric; sparsest cut", } @Article{Chuzhoy:2008:ASN, author = "Julia Chuzhoy and Anupam Gupta and Joseph (Seffi) Naor and Amitabh Sinha", title = "On the approximability of some network design problems", journal = j-TALG, volume = "4", number = "2", pages = "23:1--23:??", month = may, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1361192.1361200", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:51 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Consider the following classical network design problem: a set of terminals {$ T = \{ t_i \} $} wishes to send traffic to a root {$r$} in an {$n$}-node graph {$ G = (V, E) $}. Each terminal {$ t_i $} sends {$ d_i $} units of traffic and enough bandwidth has to be allocated on the edges to permit this. However, bandwidth on an edge {$e$} can only be allocated in integral multiples of some base capacity $ u_e $ and hence provisioning $ k {\times } u_e $ bandwidth on edge $e$ incurs a cost of $ \lceil k \rceil $ times the cost of that edge. The objective is a minimum-cost feasible solution.\par This is one of many network design problems widely studied where the bandwidth allocation is governed by side constraints: edges can only allow a subset of cables to be purchased on them or certain quality-of-service requirements may have to be met.\par In this work, we show that this problem and, in fact, several basic problems in this general network design framework cannot be approximated better than {$ \Omega (\log \log n) $} unless {$ {\rm NP} \subseteq {\rm DTIME}(n O(\log \log \log n)) $}, where {$ |V| = n $}. In particular, we show that this inapproximability threshold holds for (i) the Priority-Steiner Tree problem, (ii) the (single-sink) Cost-Distance problem, and (iii) the single-sink version of an even more fundamental problem, Fixed Charge Network Flow. Our results provide a further breakthrough in the understanding of the level of complexity of network design problems. These are the first nonconstant hardness results known for all these problems.", acknowledgement = ack-nhfb, articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "cost-distance; fixed charge network flow; Hardness of approximation; network design; priority Steiner tree", } @Article{Immorlica:2008:LCM, author = "Nicole Immorlica and Mohammad Mahdian and Vahab S. Mirrokni", title = "Limitations of cross-monotonic cost-sharing schemes", journal = j-TALG, volume = "4", number = "2", pages = "24:1--24:??", month = may, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1361192.1361201", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:51 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A cost-sharing scheme is a set of rules defining how to share the cost of a service (often computed by solving a combinatorial optimization problem) among serviced customers. A cost-sharing scheme is cross-monotonic if it satisfies the property that everyone is better off when the set of people who receive the service expands. In this article, we develop a novel technique for proving upper bounds on the budget-balance factor of cross-monotonic cost-sharing schemes or the worst-case ratio of recovered cost to total cost. We apply this technique to games defined, based on several combinatorial optimization problems, including the problems of edge cover, vertex cover, set cover, and metric facility location and, in each case, derive tight or nearly-tight bounds. In particular, we show that for the facility location game, there is no cross-monotonic cost-sharing scheme that recovers more than a third of the total cost. This result, together with a recent 1/3-budget-balanced cross-monotonic cost-sharing scheme of P{\'a}l and Tardos [2003] closes the gap for the facility location game. For the vertex cover and set cover games, we show that no cross-monotonic cost-sharing scheme can recover more than a {$ O(n - 1 / 3) $} and {$ O(1 / n) $} fraction of the total cost, respectively. Finally, we study the implications of our results on the existence of group-strategyproof mechanisms. We show that every group-strategyproof mechanism corresponds to a cost-sharing scheme that satisfies a condition weaker than cross-monotonicity. Using this, we prove that group-strategyproof mechanisms satisfying additional properties give rise to cross-monotonic cost-sharing schemes and therefore our upper bounds hold.", acknowledgement = ack-nhfb, articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Cross-monotonic cost-sharing schemes; group-strategyproof mechanism design; probabilistic method", } @Article{Dinitz:2008:OAS, author = "Yefim Dinitz and Shay Solomon", title = "Optimality of an algorithm solving the {Bottleneck Tower of Hanoi} problem", journal = j-TALG, volume = "4", number = "3", pages = "25:1--25:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367065", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the Bottleneck Tower of Hanoi puzzle posed by D. Wood in 1981. There, a relaxed placement rule allows a larger disk to be placed {\em higher\/} than a smaller one if their size difference is less than a pregiven value $k$. A shortest sequence of moves (optimal algorithm) transferring all the disks placed on some peg in decreasing order of size, to another peg in the same order is in question. In 1992, D. Poole suggested a natural disk-moving strategy for this problem, and computed the length of the shortest move sequence under its framework. However, other strategies were overlooked, so the lower bound/optimality question remained open. In 1998, Benditkis, Berend, and Safro proved the optimality of Poole's algorithm for the first nontrivial case $ k = 2 $. We prove Poole's algorithm to be optimal in the general case.", acknowledgement = ack-nhfb, articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Optimality proofs; Tower of Hanoi", } @Article{Alonso:2008:DP, author = "Laurent Alonso and Edward M. Reingold", title = "Determining plurality", journal = j-TALG, volume = "4", number = "3", pages = "26:1--26:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367066", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a set of $n$ elements, each of which is colored one of $c$ colors, we must determine an element of the plurality (most frequently occurring) color by pairwise equal/unequal color comparisons of elements. We prove that $ (c - 1)(n - c) / 2 $ color comparisons are necessary in the worst case to determine the plurality color and give an algorithm requiring {$ (0.775 c + 5.9) n + O(c^2) $} color comparisons for {$ c \geq 9 $}.", acknowledgement = ack-nhfb, articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Algorithm analysis; majority problem; plurality problem", } @Article{Alonso:2008:ACL, author = "Laurent Alonso and Edward M. Reingold", title = "Average-case lower bounds for the plurality problem", journal = j-TALG, volume = "4", number = "3", pages = "27:1--27:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367067", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a set of $n$ elements, each of which is colored one of $ c \geq 2 $ colors, we have to determine an element of the plurality (most frequently occurring) color by pairwise equal/unequal color comparisons of elements. We derive lower bounds for the expected number of color comparisons when the $ c^n $ colorings are equally probable. We prove a general lower bound of {$ c / 3 n - O(\sqrt n) $} for {$ c \geq 2 $}; we prove the stronger particular bounds of {$ 7 / 6 n - O(\sqrt n) $} for {$ c = 3 $}, {$ 54 / 35 n - O(\sqrt n) $} for {$ c = 4 $}, {$ 607 / 315 n O(\sqrt n) $} for {$ c = 5 $}, {$ 1592 / 693 n - O(\sqrt n) $} for {$ c = 6 $}, {$ 7985 / 3003 n - O(\sqrt n) $} for {$ c = 7 $}, and {$ 19402 / 6435 n - O(\sqrt n) $} for {$ c = 8 $}.", acknowledgement = ack-nhfb, articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Algorithm analysis; majority problem; plurality problem", } @Article{Lu:2008:BPS, author = "Hsueh-I Lu and Chia-Chi Yeh", title = "Balanced parentheses strike back", journal = j-TALG, volume = "4", number = "3", pages = "28:1--28:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367068", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "An {\em ordinal tree\/} is an arbitrary rooted tree where the children of each node are ordered. Succinct representations for ordinal trees with efficient query support have been extensively studied. The best previously known result is due to Geary et al. [2004b, pages 1--10]. The number of bits required by their representation for an $n$-node ordinal tree {$T$} is {$ 2 n + o(n) $}, whose first-order term is information-theoretically optimal. Their representation supports a large set of {$ O(1) $}-time queries on {$T$}. Based upon a balanced string of {$ 2 n $} parentheses, we give an improved {$ 2 n + o(n) $}-bit representation for {$T$}. Our improvement is two-fold: First, the set of {$ O(1) $}-time queries supported by our representation is a proper superset of that supported by the representation of Geary, Raman, and Raman. Second, it is also much easier for our representation to support new queries by simply adding new auxiliary strings.", acknowledgement = ack-nhfb, articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Succinct data structures; XML document representation", } @Article{Roditty:2008:RSR, author = "Iam Roditty and Mikkel Thorup and Uri Zwick", title = "Roundtrip spanners and roundtrip routing in directed graphs", journal = j-TALG, volume = "4", number = "3", pages = "29:1--29:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367069", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce the notion of {\em roundtrip-spanners\/} of weighted {\em directed\/} graphs and describe efficient algorithms for their construction. We show that for every integer $ k \geq 1 $ and any $ \epsilon > 0 $, any directed graph on $n$ vertices with edge weights in the range {$ [1, W] $} has a {$ (2 k + \epsilon) $}-roundtrip-spanner with {$ O(\min (k^2 / \epsilon)) n^{1 + 1 / k} (\log (n W), (k / \epsilon)^2 n^{1 + 1 / k}, (\log n)^{2 - 1 / k}) $} edges. We then extend these constructions and obtain compact roundtrip routing schemes. For every integer {$ k \geq 1 $} and every {$ \epsilon > 0 $}, we describe a roundtrip routing scheme that has stretch {$ 4 k + \epsilon $}, and uses at each vertex a routing table of size {$ \tilde {O}((k^2 / \epsilon) n^{1 / k} \log (n W)) $}. We also show that any weighted directed graph with {\em arbitrary / \/} positive edge weights has a 3-roundtrip-spanner with {$ O(n^{3 / 2}) $} edges. This result is optimal. Finally, we present a stretch 3 roundtrip routing scheme that uses local routing tables of size {$ \tilde {O}(n^{1 / 2}) $}. This routing scheme is essentially optimal. The roundtrip-spanner constructions and the roundtrip routing schemes for directed graphs that we describe are only slightly worse than the best available spanners and routing schemes for undirected graphs. Our roundtrip routing schemes substantially improve previous results of Cowen and Wagner. Our results are obtained by combining ideas of Cohen, Cowen and Wagner, Thorup and Zwick, with some new ideas.", acknowledgement = ack-nhfb, articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "distances; roundtrip; Routing; shortest paths; spanners", } @Article{Gu:2008:OBD, author = "Qian-Ping Gu and Hisao Tamaki", title = "Optimal branch-decomposition of planar graphs in {$ O(n^3) $} time", journal = j-TALG, volume = "4", number = "3", pages = "30:1--30:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367070", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give an {$ O(n^3) $} time algorithm for constructing a minimum-width branch-decomposition of a given planar graph with {$n$} vertices. This is achieved through a refinement to the previously best known algorithm of Seymour and Thomas, which runs in {$ O(n^4) $} time.", acknowledgement = ack-nhfb, articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Branch-decompositions; planar graphs", } @Article{Czumaj:2008:TEM, author = "Artur Czumaj and Christian Sohler", title = "Testing {Euclidean} minimum spanning trees in the plane", journal = j-TALG, volume = "4", number = "3", pages = "31:1--31:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367071", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a Euclidean graph {$G$} over a set {$P$} of {$n$} points in the plane, we are interested in verifying whether {$G$} is a Euclidean minimum spanning tree (EMST) of {$P$} or {$G$} differs from it in more than {$ \epsilon n $} edges. We assume that {$G$} is given in adjacency list representation and the point/vertex set {$P$} is given in an array. We present a property testing algorithm that accepts graph {$G$} if it is an EMST of {$P$} and that rejects with probability at least {$ 2 / 3 $} if {$G$} differs from every EMST of {$P$} in more than {$ \epsilon, n $} edges. Our algorithm runs in {$ O(\sqrt n / \epsilon \cdot \log^2 (n / \epsilon)) $} time and has a query complexity of {$ O(\sqrt n / \epsilon \cdot \log (n / \epsilon)) $}.", acknowledgement = ack-nhfb, articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Euclidean minimum spanning tree; property testing; randomized algorithms", } @Article{Makinen:2008:DEC, author = "Veli M{\"a}kinen and Gonzalo Navarro", title = "Dynamic entropy-compressed sequences and full-text indexes", journal = j-TALG, volume = "4", number = "3", pages = "32:1--32:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367072", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give new solutions to the Searchable Partial Sums with Indels problem. Given a sequence of $n$ $k$-bit numbers, we present a structure taking $ k n + o(k n) $ bits of space, able of performing operations {\em sum}, {\em search}, {\em insert}, and {\em delete}, all in {$ O(\log n) $} worst-case time, for any {$ k = O(\log n) $}. This extends previous results by Hon et al. [2003c] achieving the same space and {$ O(\log n / \log \log n) $} time complexities for the queries, yet offering complexities for {\em insert\/} and {\em delete\/} that are amortized and worse than ours, and supported only for {$ k = O(1) $}. Our result matches an existing lower bound for large values of {$k$}.\par We also give new solutions to the Dynamic Sequence problem. Given a sequence of {$n$} symbols in the range {$ [1, \sigma] $} with binary zero-order entropy {$ H_0 $}, we present a dynamic data structure that requires {$ n_0 + o(n \log \sigma) $} bits of space, which is able of performing {\em rank\/} and {\em select}, as well as inserting and deleting symbols at arbitrary positions, in {$ O(\log n \log \sigma) $} time. Our result is the {\em first\/} entropy-bound dynamic data structure for {\em rank\/} and {\em select\/} over general sequences.\par In the case {$ \sigma = 2 $}, where both previous problems coincide, we improve the dynamic solution of Hon et al. [2003c] in that we compress the sequence. The only previous result with entropy-bound space for dynamic binary sequences is by Blandford and Blelloch [2004], which has the same complexities as our structure, but does not achieve constant 1 multiplying the entropy term in the space complexity.\par Finally, we present a new dynamic compressed full-text self-index, for a collection of texts over an alphabet of size {$ \sigma $}, of overall length {$n$} and $h$ th order empirical entropy {$ H_h $}. The index requires {$ n H_h + o(n \log \sigma) $} bits of space, for any {$ h \leq \alpha \log_\sigma n $} and constant {$0$}.\par An important result we prove in this paper is that the wavelet tree of the Burrows--Wheeler transform of a text, if compressed with a technique that achieves zero-order compression locally (e.g., Raman et al. [2002]), automatically achieves $h$ th order entropy space for any $h$. This unforeseen relation is essential for the results of the previous paragraph, but it also derives into significant simplifications on many existing static compressed full-text self-indexes that build on wavelet trees.", acknowledgement = ack-nhfb, articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Compressed dynamic data structures; compressed text databases; entropy; partial sums; sequences", } @Article{Kowalski:2008:WAD, author = "Dariusz R. Kowalski and Alexander A. Shvartsman", title = "Writing-all deterministically and optimally using a nontrivial number of asynchronous processors", journal = j-TALG, volume = "4", number = "3", pages = "33:1--33:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367073", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The problem of performing $n$ tasks on $p$ asynchronous or undependable processors is a basic problem in distributed computing. This article considers an abstraction of this problem called {\em Write-All: using $p$ processors write 1's into all locations of an array of size n}. In this problem writing 1 abstracts the notion of performing a simple task. Despite substantial research, there is a dearth of efficient deterministic asynchronous algorithms for {\em Write-All/}. Efficiency of algorithms is measured in terms of {\em work\/} that accounts for all local steps performed by the processors in solving the problem. Thus, an optimal algorithm would have work {$ \Theta (n) $}, however it is known that optimality cannot be achieved when {$ p = \Omega (n) $}. The quest then is to obtain work-optimal solutions for this problem using a nontrivial, compared to {$n$}, number of processors {$p$}. The algorithm presented in this article has work complexity of {$ O(n + p^{2 + \epsilon }) $}, and it achieves work optimality for {$ p = O(n^{1 / (2 + \epsilon)}) $} for any {$ \epsilon > 0 $}, while the previous best result achieved optimality for {$ p \leq 4 \sqrt n / \log n $}. Additionally, the new result uses {\em only\/} the atomic read/write memory, without resorting to using the test-and-set primitive that was necessary in the previous solution.", acknowledgement = ack-nhfb, articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Asynchrony; distributed algorithms; shared memory; work; Write-All", } @Article{Even:2008:ACR, author = "Guy Even and Retsef Levi and Dror Rawitz and Baruch Schieber and Shimon (Moni) Shahar and Maxim Sviridenko", title = "Algorithms for capacitated rectangle stabbing and lot sizing with joint set-up costs", journal = j-TALG, volume = "4", number = "3", pages = "34:1--34:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367074", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the rectangle stabbing problem, we are given a set of axis parallel rectangles and a set of horizontal and vertical lines, and our goal is to find a minimum size subset of lines that intersect all the rectangles. In this article, we study the capacitated version of this problem in which the input includes an integral capacity for each line. The capacity of a line bounds the number of rectangles that the line can cover. We consider two versions of this problem. In the first, one is allowed to use only a single copy of each line ({\em hard capacities\/}), and in the second, one is allowed to use multiple copies of every line, but the multiplicities are counted in the size (or weight) of the solution ({\em soft capacities\/}).\par We present an exact polynomial-time algorithm for the weighted one dimensional case with hard capacities that can be extended to the one dimensional weighted case with soft capacities. This algorithm is also extended to solve a certain capacitated multi-item {\em lot-sizing\/} inventory problem with joint set-up costs. For the case of $d$-dimensional rectangle stabbing with soft capacities, we present a $ 3 d $-approximation algorithm for the unweighted case. For $d$-dimensional rectangle stabbing problem with hard capacities, we present a bi-criteria algorithm that computes $ 4 d $-approximate solutions that use at most two copies of every line. Finally, we present hardness results for rectangle stabbing when the dimension is part of the input and for a two-dimensional weighted version with hard capacities.", acknowledgement = ack-nhfb, articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; capacitated covering; lot sizing; rectangle stabbing", } @Article{Zhang:2008:CCP, author = "Cun-Quan Zhang and Yongbin Ou", title = "Clustering, community partition and disjoint spanning trees", journal = j-TALG, volume = "4", number = "3", pages = "35:1--35:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367075", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Clustering method is one of the most important tools in statistics. In a graph theory model, clustering is the process of finding all dense subgraphs. A mathematically well-defined measure for graph density is introduced in this article as follows. Let {$ G = (V, E) $} be a graph (or multi-graph) and {$H$} be a subgraph of {$G$}. The dynamic density of {$H$} is the greatest integer {$k$} such that {$ \min_\forall P \{ | E (H / P)| / | V (H / P)| - 1 \} > k $} where the minimum is taken over all possible partitions {$P$} of the vertex set of {$H$}, and {$ H / P $} is the graph obtained from {$H$} by contracting each part of {$P$} into a single vertex. A subgraph {$H$} of {$G$} is a level-{$k$} community if {$H$} is a maximal subgraph of {$G$} with dynamic density at least {$k$}. An algorithm is designed in this paper to detect all level-{$h$} communities of an input multi-graph {$G$}. The worst-case complexity of this algorithm is upper bounded by {$ O(|V(G)|^2 h^2) $}. This new method is one of few available clustering methods that are mathematically well-defined, supported by rigorous mathematical proof and able to achieve the optimization goal with polynomial complexity. As a byproduct, this algorithm also can be applied for finding edge-disjoint spanning trees of a multi-graph. The worst-case complexity is lower than all known algorithms for multi-graphs.", acknowledgement = ack-nhfb, articleno = "35", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "clustering; community; dense subgraph; dynamic density; hierarchical clustering; polynomial algorithm; Spanning trees", } @Article{Yu:2008:IAM, author = "Hung-I. Yu and Tzu-Chin Lin and Biing-Feng Wang", title = "Improved algorithms for the minmax-regret 1-center and 1-median problems", journal = j-TALG, volume = "4", number = "3", pages = "36:1--36:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367076", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, efficient algorithms are presented for the minmax-regret 1-center and 1-median problems on a general graph and a tree with uncertain vertex weights. For the minmax-regret 1-center problem on a general graph, we improve the previous upper bound from {$ O(m n^2 \log n) $} to {$ O(m n \log n) $}. For the problem on a tree, we improve the upper bound from {$ O(n^2) $} to {$ O(n \log^2 n) $}. For the minmax-regret 1-median problem on a general graph, we improve the upper bound from {$ O(m n^2 \log n) $} to {$ O(m n^2 + n^3 \log n) $}. For the problem on a tree, we improve the upper bound from {$ O(n \log^2 n) $} to {$ O(n \log n) $}.", acknowledgement = ack-nhfb, articleno = "36", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "centers; general graphs; Location theory; medians; minmax-regret optimization; trees", } @Article{Abraham:2008:CNI, author = "Ittai Abraham and Cyril Gavoille and Dahlia Malkhi and Noam Nisan and Mikkel Thorup", title = "Compact name-independent routing with minimum stretch", journal = j-TALG, volume = "4", number = "3", pages = "37:1--37:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367077", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a weighted undirected network with arbitrary node names, we present a compact routing scheme, using a {$ \tilde {O}(\sqrt n) $} space routing table at each node, and routing along paths of stretch 3, that is, at most thrice as long as the minimum cost paths. This is optimal in a very strong sense. It is known that no compact routing using {$ o(n) $} space per node can route with stretch below 3. Also, it is known that any stretch below 5 requires {$ \Omega (\sqrt n) $} space per node.", acknowledgement = ack-nhfb, articleno = "37", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Compact routing", } @Article{Pruhs:2008:GBR, author = "Kirk Pruhs and Patchrawat Uthaisombut and Gerhard Woeginger", title = "Getting the best response for your erg", journal = j-TALG, volume = "4", number = "3", pages = "38:1--38:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367078", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the speed scaling problem of minimizing the average response time of a collection of dynamically released jobs subject to a constraint {$A$} on energy used. We propose an algorithmic approach in which an energy optimal schedule is computed for a huge {$A$}, and then the energy optimal schedule is maintained as {$A$} decreases. We show that this approach yields an efficient algorithm for equi-work jobs. We note that the energy optimal schedule has the surprising feature that the job speeds are not monotone functions of the available energy. We then explain why this algorithmic approach is problematic for arbitrary work jobs. Finally, we explain how to use the algorithm for equi-work jobs to obtain an algorithm for arbitrary work jobs that is {$ O(1) $}-approximate with respect to average response time, given an additional factor of {$ (1 + \epsilon) $} energy.", acknowledgement = ack-nhfb, articleno = "38", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "frequency scaling; power management; scheduling; Speed scaling; voltage scaling", } @Article{Ajwani:2008:AIT, author = "Deepak Ajwani and Tobias Friedrich and Ulrich Meyer", title = "An {$ O(n^{2.75}) $} algorithm for incremental topological ordering", journal = j-TALG, volume = "4", number = "4", pages = "39:1--39:??", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383370", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a simple algorithm which maintains the topological order of a directed acyclic graph (DAG) with $n$ nodes, under an online edge insertion sequence, in {$ O(n^{2.75}) $} time, independent of the number {$m$} of edges inserted. For dense DAGs, this is an improvement over the previous best result of {$ O(\min m^{3 / 2} \log n, m^{3 / 2} + n^2 \log n) $} by Katriel and Bodlaender [2006]. We also provide an empirical comparison of our algorithm with other algorithms for incremental topological sorting.", acknowledgement = ack-nhfb, articleno = "39", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Dynamic algorithms; graphs; online algorithms; topological order", } @Article{Ibarra:2008:FDA, author = "Louis Ibarra", title = "Fully dynamic algorithms for chordal graphs and split graphs", journal = j-TALG, volume = "4", number = "4", pages = "40:1--40:??", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383371", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present the first dynamic algorithm that maintains a clique tree representation of a chordal graph and supports the following operations: (1) query whether deleting or inserting an arbitrary edge preserves chordality; and (2) delete or insert an arbitrary edge, provided it preserves chordality. We give two implementations. In the first, each operation runs in {$ O(n) $} time, where {$n$} is the number of vertices. In the second, an insertion query runs in {$ O(\log^2 n) $} time, an insertion in {$ O(n) $} time, a deletion query in {$ O(n) $} time, and a deletion in {$ O(n \log n) $} time. We also present a data structure that allows a deletion query to run in {$ O(\sqrt m) $} time in either implementation, where {$m$} is the current number of edges. Updating this data structure after a deletion or insertion requires {$ O(m) $} time.\par We also present a very simple dynamic algorithm that supports each of the following operations in {$ O(1) $} time on a general graph: (1) query whether the graph is split, and (2) delete or insert an arbitrary edge.", acknowledgement = ack-nhfb, articleno = "40", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "chordal graphs; clique trees; Dynamic graph algorithms; split graphs", } @Article{Korman:2008:DRS, author = "Amos Korman and David Peleg", title = "Dynamic routing schemes for graphs with low local density", journal = j-TALG, volume = "4", number = "4", pages = "41:1--41:??", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383372", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article studies approximate distributed routing schemes on dynamic communication networks. The work focuses on dynamic weighted general graphs where the vertices of the graph are fixed, but the weights of the edges may change. Our main contribution concerns bounding the cost of adapting to dynamic changes. The update efficiency of a routing scheme is measured by the time needed in order to update the routing scheme following a weight change. A naive dynamic routing scheme, which updates all vertices following a weight change, requires {$ \Omega (\hbox {\em Diam \/ }) $} time in order to perform the updates after every weight change, where {\em Diam\/} is the diameter of the underlying graph. In contrast, this article presents approximate dynamic routing schemes with average time complexity {$ \tilde {\Theta }(d) $} per topological change, where {$d$} is the local density parameter of the underlying graph. Following a weight change, our scheme never incurs more than {\em Diam\/} time; thus, our scheme is particularly efficient on graphs which have low local density and large diameter. The article also establishes upper and lower bounds on the size of the databases required by the scheme at each site.", acknowledgement = ack-nhfb, articleno = "41", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "distributed algorithms; dynamic networks; Routing schemes", } @Article{Cohen:2008:LGG, author = "Reuven Cohen and Pierre Fraigniaud and David Ilcinkas and Amos Korman and David Peleg", title = "Label-guided graph exploration by a finite automaton", journal = j-TALG, volume = "4", number = "4", pages = "42:1--42:??", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383373", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A finite automaton, simply referred to as a {\em robot}, has to explore a graph, that is, visit all the nodes of the graph. The robot has no a priori knowledge of the topology of the graph, nor of its size. It is known that for any $k$-state robot, there exists a graph of maximum degree 3 that the robot cannot explore. This article considers the effects of allowing the system designer to add short labels to the graph nodes in a preprocessing stage, for helping the exploration by the robot. We describe an exploration algorithm that, given appropriate 2-bit labels (in fact, only 3-valued labels), allows a robot to explore all graphs. Furthermore, we describe a suitable labeling algorithm for generating the required labels in linear time. We also show how to modify our labeling scheme so that a robot can explore all graphs of bounded degree, given appropriate 1-bit labels. In other words, although there is no robot able to explore all graphs of maximum degree 3, there is a robot {$R$}, and a way to color in black or white the nodes of any bounded-degree graph {$G$}, so that {$R$} can explore the colored graph {$G$}. Finally, we give impossibility results regarding graph exploration by a robot with no internal memory (i.e., a single-state automaton).", acknowledgement = ack-nhfb, articleno = "42", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Distributed algorithms; graph exploration; labeling schemes", } @Article{Suzuki:2008:DSP, author = "Akiko Suzuki and Takeshi Tokuyama", title = "Dense subgraph problems with output-density conditions", journal = j-TALG, volume = "4", number = "4", pages = "43:1--43:??", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383374", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the dense subgraph problem that extracts a subgraph, with a prescribed number of vertices, having the maximum number of edges (or total edge weight, in the weighted case) in a given graph. We give approximation algorithms with improved theoretical approximation ratios assuming that the density of the optimal output subgraph is high, where density is the ratio of number of edges (or sum of edge weights) to the number of edges in the clique on the same number of vertices. Moreover, we investigate the case where the input graph is bipartite and design a randomized pseudopolynomial time approximation scheme that can become a randomized PTAS, even if the size of the optimal output graph is comparatively small. This is a significant improvement in a theoretical sense, since no constant-ratio approximation algorithm was known previously if the output graph has o(n) vertices.", acknowledgement = ack-nhfb, articleno = "43", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithms; Combinatorial optimization; dense subgraph; randomized algorithms", } @Article{Bar-Noy:2008:DCF, author = "Amotz Bar-Noy and Panagiotis Cheilaris and Shakhar Smorodinsky", title = "Deterministic conflict-free coloring for intervals: {From} offline to online", journal = j-TALG, volume = "4", number = "4", pages = "44:1--44:18", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383375", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We investigate deterministic algorithms for a frequency assignment problem in cellular networks. The problem can be modeled as a special vertex coloring problem for hypergraphs: In every hyperedge there must exist a vertex with a color that occurs exactly once in the hyperedge (the conflict-free property). We concentrate on a special case of the problem, called conflict-free coloring for intervals. We introduce a hierarchy of four models for the aforesaid problem: (i) static, (ii) dynamic offline, (iii) dynamic online with absolute positions, and (iv) dynamic online with relative positions. In the dynamic offline model, we give a deterministic algorithm that uses at most $ \log_{3 / 2} n + 1 \approx 1.71 \log_2 n $ colors and show inputs that force any algorithm to use at least $ 3 \log_5 n + 1 \approx 1.29 \log_2 n $ colors. For the online absolute-positions model, we give a deterministic algorithm that uses at most $ 3 \lceil \log_3 n \rceil \approx 1.89 \log_2 n $ colors. To the best of our knowledge, this is the first deterministic online algorithm using {$ O(\log n) $} colors in a nontrivial online model. In the online relative-positions model, we resolve an open problem by showing a tight analysis on the number of colors used by the first-fit greedy online algorithm. We also consider conflict-free coloring only with respect to intervals that contain at least one of the two extreme points.", acknowledgement = ack-nhfb, articleno = "44", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "cellular networks; coloring; conflict free; frequency assignment; Online algorithms", } @Article{Chandran:2008:IAO, author = "Nishanth Chandran and Ryan Moriarty and Rafail Ostrovsky and Omkant Pandey and Mohammad Ali Safari and Amit Sahai", title = "Improved algorithms for optimal embeddings", journal = j-TALG, volume = "4", number = "4", pages = "45:1--45:14", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383376", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the last decade, the notion of metric embeddings with small distortion has received wide attention in the literature, with applications in combinatorial optimization, discrete mathematics, and bio-informatics. The notion of embedding is, given two metric spaces on the same number of points, to find a bijection that minimizes maximum Lipschitz and bi-Lipschitz constants. One reason for the popularity of the notion is that algorithms designed for one metric space can be applied to a different one, given an embedding with small distortion. The better distortion, the better the effectiveness of the original algorithm applied to a new metric space.\par The goal recently studied by Kenyon et al. [2004] is to consider all possible embeddings between two {\em finite\/} metric spaces and to find the best possible one; that is, consider a single objective function over the space of all possible embeddings that minimizes the distortion. In this article we continue this important direction. In particular, using a theorem of Albert and Atkinson [2005], we are able to provide an algorithm to find the optimal bijection between two line metrics, provided that the optimal distortion is smaller than 13.602. This improves the previous bound of $ 3 + 2 \sqrt {2} $, solving an open question posed by Kenyon et al. [2004]. Further, we show an inherent limitation of algorithms using the ``forbidden pattern'' based dynamic programming approach, in that they cannot find optimal mapping if the optimal distortion is more than $ 7 + 4 \sqrt {3} (\simeq 13.928) $. Thus, our results are almost optimal for this method. We also show that previous techniques for general embeddings apply to a (slightly) more general class of metrics.", acknowledgement = ack-nhfb, articleno = "45", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "dynamic programming; forbidden patterns; line embeddings; metric spaces; Optimal metric embeddings; shape matching", } @Article{Alon:2008:OEM, author = "Noga Alon and Mihai B{\~a}doiu and Erik D. Demaine and Martin Farach-Colton and Mohammadtaghi Hajiaghayi and Anastasios Sidiropoulos", title = "Ordinal embeddings of minimum relaxation: {General} properties, trees, and ultrametrics", journal = j-TALG, volume = "4", number = "4", pages = "46:1--46:??", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383377", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce a new notion of embedding, called {\em minimum-relaxation ordinal embedding}, parallel to the standard notion of minimum-distortion (metric) embedding. In an ordinal embedding, it is the relative order between pairs of distances, and not the distances themselves, that must be preserved as much as possible. The (multiplicative) relaxation of an ordinal embedding is the maximum ratio between two distances whose relative order is inverted by the embedding. We develop several worst-case bounds and approximation algorithms on ordinal embedding. In particular, we establish that ordinal embedding has many qualitative differences from metric embedding, and we capture the ordinal behavior of ultrametrics and shortest-path metrics of unweighted trees.", acknowledgement = ack-nhfb, articleno = "46", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "distortion; Metrics; ordinal embedding; relaxation", } @Article{Blaser:2008:NAA, author = "Markus Bl{\"a}ser", title = "A new approximation algorithm for the asymmetric {TSP} with triangle inequality", journal = j-TALG, volume = "4", number = "4", pages = "47:1--47:??", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383378", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a polynomial time factor $ 0.999 \cdot \log n $ approximation algorithm for the asymmetric traveling salesperson problem with triangle inequality.", acknowledgement = ack-nhfb, articleno = "47", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithm; cycle cover; traveling salesman problem; TSP", } @Article{Boyar:2008:RWO, author = "Joan Boyar and Paul Medvedev", title = "The relative worst order ratio applied to seat reservation", journal = j-TALG, volume = "4", number = "4", pages = "48:1--48:??", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383379", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The seat reservation problem is the problem of assigning passengers to seats on a train with $n$ seats and $k$ stations enroute in an online manner. The performance of algorithms for this problem is studied using the relative worst order ratio, a fairly new measure for the quality of online algorithms, which allows for direct comparisons between algorithms. This study has yielded new separations between algorithms. For example, for both variants of the problem considered, using the relative worst order ratio, First-Fit and Best-Fit are shown to be better than Worst-Fit.", acknowledgement = ack-nhfb, articleno = "48", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Online; quality measure; relative worst order ratio; seat reservation", } @Article{Nieberg:2008:ASW, author = "Tim Nieberg and Johann Hurink and Walter Kern", title = "Approximation schemes for wireless networks", journal = j-TALG, volume = "4", number = "4", pages = "49:1--49:??", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383380", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Wireless networks are created by the communication links between a collection of radio transceivers. The nature of wireless transmissions does not lead to arbitrary undirected graphs but to structured graphs which we characterize by the polynomially bounded growth property. In contrast to many existing graph models for wireless networks, the property of polynomially bounded growth is defined independently of geometric data such as positional information.\par On such wireless networks, we present an approach that can be used to create polynomial-time approximation schemes for several optimization problems called the local neighborhood-based scheme. We apply this approach to the problems of seeking maximum (weight) independent sets and minimum dominating sets. These are two important problems in the area of wireless communication networks and are also used in many applications ranging from clustering to routing strategies. However, the approach is presented in a general fashion since it can be applied to other problems as well.\par The approach for the approximation schemes is robust in the sense that it accepts any undirected graph as input and either outputs a solution of desired quality or correctly asserts that the graph presented as input does not satisfy the structural assumption of a wireless network (an NP-hard problem).", acknowledgement = ack-nhfb, articleno = "49", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "bounded growth; maximum independent set; minimum dominating set; PTAS; Wireless ad-hoc networks", } @Article{Massberg:2008:AAF, author = "Jens Ma{\ss}berg and Jens Vygen", title = "Approximation algorithms for a facility location problem with service capacities", journal = j-TALG, volume = "4", number = "4", pages = "50:1--50:15", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383381", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present the first constant-factor approximation algorithms for the following problem. Given a metric space {$ (V, c) $}, a finite set {$ d \subseteq V $} of terminals\slash customers with demands {$ d : d \rightarrow \mathbb {R}_+ $}, a facility opening cost {$ f \in \mathbb {R}_+ $} and a capacity {$ u \in \mathbb {R}_+ $}, find a partition {$ d = D_1 \dot {\cup } \cdots {} \dot {\cup } D_k $} and Steiner trees {$ T_i $} for {$ D_i (i = 1, \ldots {}, k) $} with {$ c(E(T_i)) + d(D_i) \leq u $} for {$ i = 1, \ldots {}, k $} such that {$ \sum_{i = 1}^k c(E(T_i)) + k f $} is minimum. This problem arises in VLSI design. It generalizes the bin-packing problem and the Steiner tree problem. In contrast to other network design and facility location problems, it has the additional feature of upper bounds on the service cost that each facility can handle. Among other results, we obtain a 4.1-approximation in polynomial time, a 4.5-approximation in cubic time, and a 5-approximation as fast as computing a minimum spanning tree on {$ (D, c) $}.", acknowledgement = ack-nhfb, articleno = "50", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithm; facility location; network design; VLSI design", } @Article{Swamy:2008:FTF, author = "Chaitanya Swamy and David B. Shmoys", title = "Fault-tolerant facility location", journal = j-TALG, volume = "4", number = "4", pages = "51:1--51:??", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383382", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider a fault-tolerant generalization of the classical uncapacitated facility location problem, where each client $j$ has a requirement that $ r_j $ {\em distinct\/} facilities serve it, instead of just one. We give a 2.076-approximation algorithm for this problem using LP rounding, which is currently the best-known performance guarantee. Our algorithm exploits primal and dual complementary slackness conditions and is based on {\em clustered randomized rounding}. A technical difficulty that we overcome is the presence of terms with negative coefficients in the dual objective function, which makes it difficult to bound the cost in terms of dual variables. For the case where all requirements are the same, we give a primal-dual 1.52-approximation algorithm.\par We also consider a fault-tolerant version of the $k$-median problem. In the metric $k$-median problem, we are given $n$ points in a metric space. We must select $k$ of these to be centers, and then assign each input point $j$ to the selected center that is closest to it. In the fault-tolerant version we want $j$ to be assigned to $ r_j $ distinct centers. The goal is to select the $k$ centers so as to minimize the sum of assignment costs. The primal-dual algorithm for fault-tolerant facility location with uniform requirements also yields a 4-approximation algorithm for the fault-tolerant $k$-median problem for this case. This the first constant-factor approximation algorithm for the uniform requirements case.", acknowledgement = ack-nhfb, articleno = "51", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; facility location; k-median problem", } @Article{Fotakis:2008:ACG, author = "Dimitris Fotakis and Spyros Kontogiannis and Paul Spirakis", title = "Atomic congestion games among coalitions", journal = j-TALG, volume = "4", number = "4", pages = "52:1--52:??", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383383", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider algorithmic questions concerning the existence, tractability, and quality of Nash equilibria, in atomic congestion games among users participating in selfish coalitions.\par We introduce a coalitional congestion model among atomic players and demonstrate many interesting similarities with the noncooperative case. For example, there exists a potential function proving the existence of pure Nash equilibria (PNE) in the unrelated parallel links setting; in the network setting, the finite improvement property collapses as soon as we depart from linear delays, but there is an exact potential (and thus PNE) for linear delays. The price of anarchy on identical parallel links demonstrates a quite surprising threshold behavior: It persists on being asymptotically equal to that in the case of the noncooperative KP-model, unless the number of coalitions is {\em sublogarithmic}.\par We also show crucial differences, mainly concerning the hardness of algorithmic problems that are solved efficiently in the noncooperative case. Although we demonstrate convergence to robust PNE, we also prove the hardness of computing them. On the other hand, we propose a generalized fully mixed Nash equilibrium that can be efficiently constructed in most cases. Finally, we propose a natural improvement policy and prove its convergence in pseudopolynomial time to PNE which are robust against (even dynamically forming) coalitions of small size.", acknowledgement = ack-nhfb, articleno = "52", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Algorithmic game theory; congestion games; convergence to equilibria; price of anarchy", } @Article{Torng:2008:SOU, author = "Eric Torng and Jason McCullough", title = "{SRPT} optimally utilizes faster machines to minimize flow time", journal = j-TALG, volume = "5", number = "1", pages = "1:1--1:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435376", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We analyze the shortest remaining processing time (SRPT) algorithm with respect to the problem of scheduling $n$ jobs with release times on $m$ identical machines to minimize total flow time. It is known that SRPT is optimal if $ m = 1$ but that SRPT has a worst-case approximation ratio of $ \Theta (\min (\log n / m, \log \Delta)) $ for this problem, where $ \Delta $ is the ratio of the length of the longest job divided by the length of the shortest job. It has previously been shown that SRPT is able to use faster machines to produce a schedule {\em as good as\/} an optimal algorithm using slower machines. We now show that SRPT {\em optimally\/} uses these faster machines with respect to the worst-case approximation ratio. That is, if SRPT is given machines that are $ s \geq 2 - 1 / m $ times as fast as those used by an optimal algorithm, SRPT's flow time is at least $s$ {\em times smaller\/} than the flow time incurred by the optimal algorithm. Clearly, no algorithm can offer a better worst-case guarantee, and we show that existing algorithms with similar performance guarantees to SRPT without resource augmentation do not optimally use extra resources.", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "flow time; parallel machines; resource augmentation; scheduling; SRPT", } @Article{Goldwasser:2008:ONS, author = "Michael H. Goldwasser and Mark Pedigo", title = "Online nonpreemptive scheduling of equal-length jobs on two identical machines", journal = j-TALG, volume = "5", number = "1", pages = "2:1--2:18", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435377", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the nonpreemptive scheduling of two identical machines for jobs with equal processing times yet arbitrary release dates and deadlines. Our objective is to maximize the number of jobs completed by their deadlines. Using standard nomenclature, this problem is denoted as {$ P 2 \mid p_j = p, 4_j \mid \sum {\bar {U}}_j $}. The problem is known to be polynomially solvable in an offline setting.\par In an online variant of the problem, a job's existence and parameters are revealed to the scheduler only upon that job's release date. We present an online deterministic algorithm for the problem and prove that it is {$ 3 / 2 $}-competitive. A simple lower bound shows that this is the optimal deterministic competitiveness.", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Admission control; competitive analysis; scheduling", } @Article{Aiello:2008:CBM, author = "William Aiello and Alex Kesselman and Yishay Mansour", title = "Competitive buffer management for shared-memory switches", journal = j-TALG, volume = "5", number = "1", pages = "3:1--3:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435378", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider buffer management policies for shared memory switches. We study the case of overloads resulting in packet loss, where the constraint is the limited shared memory capacity. The goal of the buffer management policy is that of maximizing the number of packets transmitted. The problem is online in nature, and thus we use competitive analysis to measure the performance of the buffer management policies. Our main result is to show that the well-known preemptive Longest Queue Drop ({\em LQD\/}) policy is at most 2-competitive and at least $ \sqrt 2 $-competitive. We also demonstrate a general lower bound of $ 4 / 3 $ on the performance of any deterministic online policy. Finally, we consider some other popular non-preemptive policies including Complete Partition, Complete Sharing, Static Threshold and Dynamic Threshold and derive almost tight bounds on their performance.", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Buffer management; competitive analysis; shared memory", } @Article{Agarwal:2008:KDD, author = "Pankaj K. Agarwal and Haim Kaplan and Micha Sharir", title = "Kinetic and dynamic data structures for closest pair and all nearest neighbors", journal = j-TALG, volume = "5", number = "1", pages = "4:1--4:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435379", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present simple, fully dynamic and kinetic data structures, which are variants of a dynamic two-dimensional range tree, for maintaining the closest pair and all nearest neighbors for a set of $n$ moving points in the plane; insertions and deletions of points are also allowed. If no insertions or deletions take place, the structure for the closest pair uses {$ O(n \log n) $} space, and processes {$ O(n^2 \beta_+ 2 (n) \log n) $} critical events, each in {$ O(\log^2 n) $} time. Here {$s$} is the maximum number of times where the distances between any two specific pairs of points can become equal, {$ \beta_s(q) = \lambda_s(q) / q $}, and {$ \lambda_s(q) $} is the maximum length of Davenport--Schinzel sequences of order $s$ on $q$ symbols. The dynamic version of the problem incurs a slight degradation in performance: If $ m \geq n $ insertions and deletions are performed, the structure still uses {$ O(n \log n) $} space, and processes {$ O(m n \beta_s + 2 (n) \log^3 n) $} events, each in {$ O(\log^3 n) $} time.\par Our kinetic data structure for all nearest neighbors uses {$ O(n \log^2 n) $} space, and processes {$ O(n^2 \beta^{2_s + 2}(n) \log^3 n) $} critical events. The expected time to process all events is {$ O(n^2 \beta_{s + 2}^2 (n) \log^4 n) $}, though processing a single event may take {$ \Theta (n) $} expected time in the worst case. If {$ m \geq n $} insertions and deletions are performed, then the expected number of events is {$ O(m n \beta^2_{s + 2}(n) \log^3 n) $} and processing them all takes {$ O(m n \beta^2_{s + 2} (n) \log^4 n) $}. An insertion or deletion takes {$ O(n) $} expected time.", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "closest pair; computational geometry; Kinetic data structures; nearest neighbors", } @Article{Agarwal:2008:ACT, author = "Pankaj K. Agarwal and Micha Sharir and Emo Welzl", title = "Algorithms for center and {Tverberg} points", journal = j-TALG, volume = "5", number = "1", pages = "5:1--5:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435380", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a set $s$ of $n$ points in {$ R^3 $}, a point {$x$} in {$ R^3 $} is called {\em center point of $S$ \/} if every closed halfspace whose bounding hyperplane passes through {$x$} contains at least {$ \lceil n / 4 \rceil $} points from {$S$}. We present a near-quadratic algorithm for computing the {\em center region}, that is the set of all center points, of a set of {$n$} points in {$ R^3 $}. This is nearly tight in the worst case since the center region can have {$ \Omega (n^2) $} complexity.\par We then consider sets {$s$} of {$ 3 n $} points in the plane which are the union of three disjoint sets consisting respectively of {$n$} red, $n$ blue, and $n$ green points. A point $x$ in {$ R^2 $} is called a {\em colored Tverberg point of $S$ \/} if there is a partition of {$s$} into {$n$} triples with one point of each color, so that {$x$} lies in all triangles spanned by these triples. We present a first polynomial-time algorithm for recognizing whether a given point is a colored Tverberg point of such a 3-colored set {$S$}.", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Arrangements; center point; Tverberg point", } @Article{Grandoni:2008:DWV, author = "Fabrizio Grandoni and Jochen K{\"o}nemann and Alessandro Panconesi", title = "Distributed weighted vertex cover via maximal matchings", journal = j-TALG, volume = "5", number = "1", pages = "6:1--6:12", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435381", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we consider the problem of computing a minimum-weight vertex-cover in an $n$-node, weighted, undirected graph {$ G = (V, E) $}. We present a fully distributed algorithm for computing vertex covers of weight at most twice the optimum, in the case of integer weights. Our algorithm runs in an expected number of {$ O(\log n + \log \hat {W}) $} communication rounds, where {$ \hat {W} $} is the average vertex-weight. The previous best algorithm for this problem requires {$ O(\log n (\log n + \log \hat {W})) $} rounds and it is not fully distributed.\par For a maximal matching {$m$} in {$G$}, it is a well-known fact that any vertex-cover in {$G$} needs to have at least {$ |m| $} vertices. Our algorithm is based on a generalization of this combinatorial lower-bound to the weighted setting.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; distributed algorithms; maximal matching; vertex cover", } @Article{Vishwanathan:2008:HIA, author = "Sundar Vishwanathan", title = "On hard instances of approximate vertex cover", journal = j-TALG, volume = "5", number = "1", pages = "7:1--7:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435382", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show that if there is a $ 2 - \epsilon $ approximation algorithm for vertex cover on graphs with vector chromatic number at most $ 2 + \delta $, then there is a $ 2 - f(\epsilon, \delta) $ approximation algorithm for vertex cover for all graphs.", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; vertex cover", } @Article{Berend:2008:CDG, author = "Daniel Berend and Steven S. Skiena and Yochai Twitto", title = "Combinatorial dominance guarantees for problems with infeasible solutions", journal = j-TALG, volume = "5", number = "1", pages = "8:1--8:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435383", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The design and analysis of approximation algorithms for {\em NP\/}-hard problems is perhaps the most active research area in the theory of combinatorial algorithms. In this article, we study the notion of a {\em combinatorial dominance guarantee\/} as a way for assessing the performance of a given approximation algorithm. An $ f(n) $ dominance bound is a guarantee that the heuristic always returns a solution not worse than at least $ f(n) $ solutions. We give tight analysis of many heuristics, and establish novel and interesting dominance guarantees even for certain inapproximable problems and heuristic search algorithms. For example, we show that the maximal matching heuristic of VERTEX COVER offers a combinatorial dominance guarantee of $ 2^n - (1.839 + o(1))^n $. We also give inapproximability results for most of the problems we discuss.", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "algorithms analysis; approximation algorithms; Computation complexity; dominance analysis", } @Article{Fomin:2008:CBM, author = "Fedor V. Fomin and Fabrizio Grandoni and Artem V. Pyatkin and Alexey A. Stepanov", title = "Combinatorial bounds via measure and conquer: {Bounding} minimal dominating sets and applications", journal = j-TALG, volume = "5", number = "1", pages = "9:1--9:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435384", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We provide an algorithm listing all minimal dominating sets of a graph on $n$ vertices in time {$ O(1.7159^n) $}. This result can be seen as an algorithmic proof of the fact that the number of minimal dominating sets in a graph on {$n$} vertices is at most {$ 1.7159^n $}, thus improving on the trivial {$ O(2^n / \sqrt n) $} bound. Our result makes use of the measure-and-conquer technique which was recently developed in the area of exact algorithms.\par Based on this result, we derive an {$ O(2.8718^n) $} algorithm for the domatic number problem.", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "domatic number; Exact exponential algorithms; listing algorithms; measure and conquer; minimum dominating set; minimum set cover", } @Article{Oum:2008:ARW, author = "Sang-Il Oum", title = "Approximating rank-width and clique-width quickly", journal = j-TALG, volume = "5", number = "1", pages = "10:1--10:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435385", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Rank-width was defined by Oum and Seymour [2006] to investigate clique-width. They constructed an algorithm that either outputs a rank-decomposition of width at most $ f(k) $ for some function f or confirms that rank-width is larger than $k$ in time {$ O(|V|^9 \log |V|) $} for an input graph {$ G = (V, E) $} and a fixed {$k$}. We develop three separate algorithms of this kind with faster running time. We construct an {$ O(|V|^4) $}-time algorithm with {$ f(k) = 3 k + 1 $} by constructing a subroutine for the previous algorithm; we avoid generic algorithms minimizing submodular functions used by Oum and Seymour. Another one is an {$ O(|V|^3) $}-time algorithm with {$ f(k) = 24 k $}, achieved by giving a reduction from graphs to binary matroids; then we use an approximation algorithm for matroid branch-width by Hlin{\^e}n{\'y} [2005]. Finally we construct an {$ O(|V|^3) $}-time algorithm with {$ f(k) = 3 k - 1 $} by combining the ideas of the two previously cited papers.", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; branch-width; clique-width; matroids; rank-width", } @Article{Brandstadt:2008:SLT, author = "Andreas Brandst{\"a}dt and Van Bang Le and R. Sritharan", title = "Structure and linear-time recognition of 4-leaf powers", journal = j-TALG, volume = "5", number = "1", pages = "11:1--11:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435386", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A graph {$G$} is the {$k$}-{\em leaf power\/} of a tree {$T$} if its vertices are leaves of {$T$} such that two vertices are adjacent in {$G$} if and only if their distance in {$T$} is at most {$k$}. Then {$T$} is a {$k$}-{\em leaf root\/} of {$G$}. This notion was introduced and studied by Nishimura, Ragde, and Thilikos [2002], motivated by the search for underlying phylogenetic trees. Their results imply an {$ O(n^3) $}-time recognition algorithm for 4-leaf powers. Recently, Rautenbach [2006] as well as Dom et al. [2005] characterized 4-leaf powers without true twins in terms of forbidden subgraphs. We give new characterizations for 4-leaf powers and squares of trees by a complete structural analysis. As a consequence, we obtain a conceptually simple linear-time recognition of 4-leaf powers.", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Graph powers; leaf powers; phylogenetic trees; squares of trees; trees", } @Article{Chen:2008:MCI, author = "Xin Chen and Lan Liu and Zheng Liu and Tao Jiang", title = "On the minimum common integer partition problem", journal = j-TALG, volume = "5", number = "1", pages = "12:1--12:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435387", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce a new combinatorial optimization problem in this article, called the {\em minimum common integer partition\/} (MCIP) problem, which was inspired by computational biology applications including ortholog assignment and DNA fingerprint assembly. A {\em partition\/} of a positive integer $n$ is a multiset of positive integers that add up to exactly $n$, and an {\em integer partition\/} of a multiset $s$ of integers is defined as the multiset union of partitions of integers in {$S$}. Given a sequence of multisets {$ s_1, s_2, \ldots, S_k $} of integers, where {$ k \geq 2 $}, we say that a multiset is a {\em common integer partition\/} if it is an integer partition of every multiset {$ S_i, 1 \leq i \leq k $}. The MCIP problem is thus defined as to find a common integer partition of {$ s_1, s_2, \ldots, S_k $} with the minimum cardinality, denoted as MCIP({$ s_1 $}, {$ S_2 $}, \ldots {}, {$ S_k $}). It is easy to see that the MCIP problem is NP-hard, since it generalizes the well-known subset sum problem. We can in fact show that it is APX-hard. We will also present a {$ 5 / 4 $}-approximation algorithm for the MCIP problem when {$ k = 2 $}, and a {$ 3 k (k - 1) / 3 k - 2 $}-approximation algorithm for $ k \geq 3 $.", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithm; combinatorial optimization; computational biology; integer partition; NP-hard; Subset sum", } @Article{Azriel:2008:IFS, author = "Dany Azriel and Noam Solomon and Shay Solomon", title = "On an infinite family of solvable {Hanoi} graphs", journal = j-TALG, volume = "5", number = "1", pages = "13:1--13:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435388", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The Tower of Hanoi problem is generalized by placing pegs on the vertices of a given directed graph {$G$} with two distinguished vertices, {$s$} and {$D$}, and allowing moves only along arcs of this graph. An optimal solution for such a graph {$G$} is an algorithm that completes the task of moving a tower of any given number of disks from {$s$} to {$d$} in a minimal number of disk moves.\par In this article we present an algorithm which solves the problem for two infinite families of graphs, and prove its optimality. To the best of our knowledge, this is the first optimality proof for an {\em infinite\/} family of graphs.\par Furthermore, we present a unified algorithm that solves the problem for a wider family of graphs and conjecture its optimality.", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Optimality proofs; Tower of Hanoi", } @Article{Elmasry:2008:MPQ, author = "Amr Elmasry and Claus Jensen and Jyrki Katajainen", title = "Multipartite priority queues", journal = j-TALG, volume = "5", number = "1", pages = "14:1--14:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435389", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce a framework for reducing the number of element comparisons performed in priority-queue operations. In particular, we give a priority queue which guarantees the worst-case cost of {$ O(1) $} per minimum finding and insertion, and the worst-case cost of {$ O(\log n) $} with at most {$ \log n + O(1) $} element comparisons per deletion, improving the bound of {$ 2 \log n + O(1) $} known for binomial queues. Here, {$n$} denotes the number of elements stored in the data structure prior to the operation in question, and {$ \log n $} equals {$ \log_2 (\max \{ 2, n \}) $}. As an immediate application of the priority queue developed, we obtain a sorting algorithm that is optimally adaptive with respect to the inversion measure of disorder, and that sorts a sequence having $n$ elements and {$I$} inversions with at most {$ n \log (I / n) + O(n) $} element comparisons.", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "constant factors; heaps; meticulous analysis; Priority queues", } @Article{Eppstein:2009:TBG, author = "David Eppstein", title = "Testing bipartiteness of geometric intersection graphs", journal = j-TALG, volume = "5", number = "2", pages = "15:1--15:??", month = mar, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1497290.1497291", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:05:00 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show how to test the bipartiteness of an intersection graph of $n$ line segments or simple polygons in the plane, or of an intersection graph of balls in $d$-dimensional Euclidean space, in time {$ O(n \log n) $}. More generally, we find subquadratic algorithms for connectivity and bipartiteness testing of intersection graphs of a broad class of geometric objects. Our algorithms for these problems return either a bipartition of the input or an odd cycle in its intersection graph. We also consider lower bounds for connectivity and {$k$}-colorability problems of geometric intersection graphs. For unit balls in {$d$} dimensions, connectivity testing has equivalent randomized complexity to construction of Euclidean minimum spanning trees, and for line segments in the plane connectivity testing has the same lower bounds as Hopcroft's point-line incidence testing problem; therefore, for these problems, connectivity is unlikely to be solved as efficiently as bipartiteness. For line segments or planar disks, testing {$k$}-colorability of intersection graphs for $k$ > 2 is NP-complete.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Bipartite graph; coin graph; disks; geometric thickness; graph coloring; Hopcroft's problem; intersection graph; line segments; minimum spanning tree", } @Article{Chen:2009:OCF, author = "Ke Chen and Haim Kaplan and Micha Sharir", title = "Online conflict-free coloring for halfplanes, congruent disks, and axis-parallel rectangles", journal = j-TALG, volume = "5", number = "2", pages = "16:1--16:??", month = mar, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1497290.1497292", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:05:00 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present randomized algorithms for online conflict-free coloring (CF in short) of points in the plane, with respect to halfplanes, congruent disks, and nearly-equal axis-parallel rectangles. In all three cases, the coloring algorithms use {$ O(\log n) $} colors, with high probability.\par We also present a deterministic algorithm for online CF coloring of points in the plane with respect to nearly-equal axis-parallel rectangles, using {$ O(\log^3 n) $} colors. This is the first efficient (i.e., using {$ \polylog (n) $} colors) deterministic online CF coloring algorithm for this problem.", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "coloring; Conflict free coloring; online algorithms", } @Article{Alonso:2009:ACA, author = "Laurent Alonso and Edward M. Reingold", title = "Average-case analysis of some plurality algorithms", journal = j-TALG, volume = "5", number = "2", pages = "17:1--17:??", month = mar, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1497290.1497293", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:05:00 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a set of $n$ elements, each of which is colored one of $c$ colors, we must determine an element of the plurality (most frequently occurring) color by pairwise equal/unequal color comparisons of elements. We focus on the expected number of color comparisons when the $ c^n $ colorings are equally probable. We analyze an obvious algorithm, showing that its expected performance is {$ c^2 + c - 2 / 2 c n - O(c^2) $}, with variance {$ \Theta (c^2 n) $}. We present and analyze an algorithm for the case {$ c = 3 $} colors whose average complexity on the {$ 3^n $} equally probable inputs is {$ 7083 / 5425 n + O(\sqrt n) = 1.3056 \ldots {} n + O(\sqrt n) $}, substantially better than the expected complexity {$ 5 / 3 n + O(1) = 1.6666 \ldots {} n + O(1) $} of the obvious algorithm. We describe a similar algorithm for {$ c = 4 $} colors whose average complexity on the {$ 4^n $} equally probable inputs is {$ 761311 / 402850 n + O(\log n) = 1.8898 \ldots {} n + O(\log n) $}, substantially better than the expected complexity {$ 9 / 4 n + O(1) = 2.25 n + O(1) $} of the obvious algorithm.", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Algorithm analysis; majority problem; plurality problem", } @Article{Bar-Noy:2009:TMR, author = "Amotz Bar-Noy and Sudipto Guha and Yoav Katz and Joseph (Seffi) Naor and Baruch Schieber and Hadas Shachnai", title = "Throughput maximization of real-time scheduling with batching", journal = j-TALG, volume = "5", number = "2", pages = "18:1--18:??", month = mar, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1497290.1497294", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:05:00 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the following scheduling with batching problem that has many applications, for example, in multimedia-on-demand and manufacturing of integrated circuits. The input to the problem consists of $n$ jobs and $k$ parallel machines. Each job is associated with a set of time intervals in which it can be scheduled (given either explicitly or nonexplicitly), a weight, and a family. Each family is associated with a processing time. Jobs that belong to the same family can be batched and executed together on the same machine. The processing time of each batch is the processing time of the family of jobs it contains. The goal is to find a nonpreemptive schedule with batching that maximizes the weight of the scheduled jobs. We give constant factor ($4$ or $ 4 + \epsilon $ ) approximation algorithms for two variants of the problem, depending on the precise representation of the input. When the batch size is unbounded and each job is associated with a time window in which it can be processed, these approximation ratios reduce to $2$ and $ 2 + \epsilon $, respectively. We also give approximation algorithms for two special cases when all release times are the same.", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "batching; local ratio technique; Scheduling", } @Article{Rabani:2009:BAT, author = "Yuval Rabani and Gabriel Scalosub", title = "Bicriteria approximation tradeoff for the node-cost budget problem", journal = j-TALG, volume = "5", number = "2", pages = "19:1--19:??", month = mar, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1497290.1497295", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:05:00 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider an optimization problem consisting of an undirected graph, with cost and profit functions defined on all vertices. The goal is to find a connected subset of vertices with maximum total profit, whose total cost does not exceed a given budget. The best result known prior to this work guaranteed a $ (2, O(\log n)) $ bicriteria approximation, that is, the solution's profit is at least a fraction of $ 1 / O(\log n) $ of an optimum solution respecting the budget, while its cost is at most twice the given budget. We improve these results and present a bicriteria tradeoff that, given any $ \epsilon \in (0, 1] $, guarantees a $ (1 + \epsilon, O(1 / \epsilon \log n)) $-approximation.", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; bicriteria approximation", } @Article{Li:2009:PTA, author = "Guojun Li and Xiaotie Deng and Ying Xu", title = "A polynomial-time approximation scheme for embedding hypergraph in a cycle", journal = j-TALG, volume = "5", number = "2", pages = "20:1--20:??", month = mar, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1497290.1497296", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:05:00 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problem of embedding hyperedges of a hypergraph as paths in a cycle such that the maximum congestion, namely the maximum number of paths that use any single edge in a cycle, is minimized.\par The {\em minimum congestion hypergraph embedding in a cycle\/} problem is known to be NP-hard and its graph version, the {\em minimum congestion graph embedding in a cycle}, is solvable in polynomial-time. Furthermore, for the graph problem, a polynomial-time approximation scheme for the weighted version is known. For the hypergraph model, several approximation algorithms with a ratio of two have been previously published. A recent paper reduced the approximation ratio to 1.5. We present a polynomial-time approximation scheme in this article, settling the debate regarding whether the problem is polynomial-time approximable.", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Hypergraph embedding; minimum congestion; NP-hard; polynomial-time approximation scheme", } @Article{Even:2009:AAA, author = "Guy Even and Jon Feldman and Guy Kortsarz and Zeev Nutov", title = "A 1.8 approximation algorithm for augmenting edge-connectivity of a graph from 1 to 2", journal = j-TALG, volume = "5", number = "2", pages = "21:1--21:??", month = mar, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1497290.1497297", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:05:00 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a 1.8-approximation algorithm for the following NP-hard problem: Given a connected graph {$ G = (V, E) $} and an edge set {$E$} on {$V$} disjoint to {$E$}, find a minimum-size subset of edges {$ F \subseteq E $} such that {$ (V, E \cup f) $} is 2-edge-connected. Our result improves and significantly simplifies the approximation algorithm with ratio {$ 1.875 + \epsilon $} of Nagamochi.", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; connectivity; graphs", } @Article{Marko:2009:ADP, author = "Sharon Marko and Dana Ron", title = "Approximating the distance to properties in bounded-degree and general sparse graphs", journal = j-TALG, volume = "5", number = "2", pages = "22:1--22:??", month = mar, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1497290.1497298", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:05:00 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We address the problem of approximating the distance of bounded-degree and general sparse graphs from having some predetermined graph property $p$. That is, we are interested in sublinear algorithms for estimating the fraction of edge modifications (additions or deletions) that must be performed on a graph so that it obtains $p$. This fraction is taken with respect to a given upper bound $m$ on the number of edges. In particular, for graphs with degree bound $d$ over $n$ vertices, $ m = d n $. To perform such an approximation the algorithm may ask for the degree of any vertex of its choice, and may ask for the neighbors of any vertex.\par The problem of estimating the distance to having a property was first explicitly addressed by Parnas et al. [2006]. In the context of graphs this problem was studied by Fischer and Newman [2007] in the dense graphs model. In this model the fraction of edge modifications is taken with respect to $ n^2 $, and the algorithm may ask for the existence of an edge between any pair of vertices of its choice. Fischer and Newman showed that every graph property that has a testing algorithm in this model, with query complexity independent of the size of the graph, also has a distance approximation algorithm with query complexity that is independent of the size of graph.\par In this work we focus on bounded-degree and general sparse graphs, and give algorithms for all properties shown to have efficient testing algorithms by Goldreich and Ron [2002]. Specifically, these properties are $k$-edge connectivity, subgraph freeness (for constant-size subgraphs), being an Eulerian graph, and cycle freeness. A variant of our subgraph-freeness algorithm approximates the size of a minimum vertex cover of a graph in sublinear time. This approximation improves on a recent result of Parnas and Ron [2007].", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "distance approximation; graph properties; property testing; Sublinear approximation algorithms", } @Article{Berry:2009:LTA, author = "Vincent Berry and Christophe Paul and Sylvain Guillemot and Fran{\c{c}}ois Nicolas", title = "Linear time 3-approximation for the {MAST} problem", journal = j-TALG, volume = "5", number = "2", pages = "23:1--23:??", month = mar, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1497290.1497299", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:05:00 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a set of leaf-labeled trees with identical leaf sets, the well-known Maximum Agreement SubTree (MAST) problem consists in finding a subtree homeomorphically included in all input trees and with the largest number of leaves. MAST and its variant called Maximum Compatible Tree (MCT) are of particular interest in computational biology. This article presents a linear-time approximation algorithm to solve the complement version of MAST, namely identifying the smallest set of leaves to remove from input trees to obtain isomorphic trees. We also present an {$ O(n^2 + k n) $} algorithm to solve the complement version of MCT. For both problems, we thus achieve significantly lower running times than previously known algorithms. Fast running times are especially important in phylogenetics where large collections of trees are routinely produced by resampling procedures, such as the nonparametric bootstrap or Bayesian MCMC methods.", acknowledgement = ack-nhfb, articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithm; maximum agreement subtree; maximum compatible subtree; phylogenetic tree", } @Article{Condon:2009:ADA, author = "Anne Condon and Amol Deshpande and Lisa Hellerstein and Ning Wu", title = "Algorithms for distributional and adversarial pipelined filter ordering problems", journal = j-TALG, volume = "5", number = "2", pages = "24:1--24:??", month = mar, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1497290.1497300", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:05:00 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Pipelined filter ordering is a central problem in database query optimization. The problem is to determine the optimal order in which to apply a given set of commutative filters (predicates) to a set of elements (the tuples of a relation), so as to find, as efficiently as possible, the tuples that satisfy all of the filters. Optimization of pipelined filter ordering has recently received renewed attention in the context of environments such as the Web, continuous high-speed data streams, and sensor networks. Pipelined filter ordering problems are also studied in areas such as fault detection and machine learning under names such as learning with attribute costs, minimum-sum set cover, and satisfying search. We present algorithms for two natural extensions of the classical pipelined filter ordering problem: (1) a {\em distributional-type\/} problem where the filters run in parallel and the goal is to maximize throughput, and (2) an {\em adversarial-type\/} problem where the goal is to minimize the expected value of {\em multiplicative regret}. We present two related algorithms for solving (1), both running in time {$ O(n^2) $}, which improve on the {$ O(n 3 \log n) $} algorithm of Kodialam. We use techniques from our algorithms for (1) to obtain an algorithm for 1.", acknowledgement = ack-nhfb, articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "flow algorithms; Pipelined filter ordering; query optimization; selection ordering", } @Article{Gabow:2009:FSI, author = "Harold Gabow", title = "Foreword to special issue on {SODA 2007}", journal = j-TALG, volume = "5", number = "3", pages = "25:1--25:??", month = jul, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1541885.1541886", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:27 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ruzic:2009:MDS, author = "Milan Ru{\v{z}}i{\'c}", title = "Making deterministic signatures quickly", journal = j-TALG, volume = "5", number = "3", pages = "26:1--26:??", month = jul, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1541885.1541887", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:27 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a new technique of universe reduction. Primary applications are the dictionary problem and the predecessor problem. We give several new results on static dictionaries in different computational models: the word RAM, the practical RAM, and the cache-oblivious model. All algorithms and data structures are deterministic and use linear space. Representative results are: a dictionary with a lookup time of {$ O(\log \log n) $} and construction time of {$ O(n) $} on sorted input on a word RAM, and a static predecessor structure for variable- and unbounded length binary strings that in the cache-oblivious model has a query performance of {$ O(| s | / B + \log | s |) $} I/Os, for query argument {$s$}.", acknowledgement = ack-nhfb, articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Carr:2009:CCN, author = "Robert D. Carr and Goran Konjevod and Greg Little and Venkatesh Natarajan and Ojas Parekh", title = "Compacting cuts: a new linear formulation for minimum cut", journal = j-TALG, volume = "5", number = "3", pages = "27:1--27:??", month = jul, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1541885.1541888", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:27 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "For a graph (V, E), existing compact linear formulations for the minimum cut problem require {$ \Theta (|V| |E|) $} variables and constraints and can be interpreted as a composition of {$ |V| - 1 $} polyhedra for minimum {$s$}--{$t$} cuts in much the same way as early approaches to finding globally minimum cuts relied on {$ |V| - 1 $} calls to a minimum {$s$}--{$t$} cut algorithm. We present the first formulation to beat this bound, one that uses {$ O(|V|^2) $} variables and {$ O(|V|^3) $} constraints. An immediate consequence of our result is a compact linear relaxation with {$ O(|V|^2) $} constraints and {$ O(|V|^3) $} variables for enforcing global connectivity constraints. This relaxation is as strong as standard cut-based relaxations and has applications in solving traveling salesman problems by integer programming as well as finding approximate solutions for survivable network design problems using Jain's iterative rounding method. Another application is a polynomial-time verifiable certificate of size {$n$} for for the NP-complete problem of {$ l_1 $}-embeddability of a rational metric on an {$n$}-set (as opposed to a certificate of size $ n^2 $ known previously).", acknowledgement = ack-nhfb, articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Giora:2009:ODV, author = "Yoav Giora and Haim Kaplan", title = "{Optimal} dynamic vertical ray shooting in rectilinear planar subdivisions", journal = j-TALG, volume = "5", number = "3", pages = "28:1--28:??", month = jul, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1541885.1541889", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:27 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the dynamic vertical ray shooting problem against horizontal disjoint segments, that is, the task of maintaining a dynamic set {$S$} of {$n$} nonintersecting horizontal line segments in the plane under a query that reports the first segment in {$S$} intersecting a vertical ray from a query point. We develop a linear-size structure that supports queries, insertions, and deletion in {$ O(\log n) $} worst-case time. Our structure works in the comparison model on a random access machine.", acknowledgement = ack-nhfb, articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Eppstein:2009:STS, author = "David Eppstein", title = "Squarepants in a tree: {Sum} of subtree clustering and hyperbolic pants decomposition", journal = j-TALG, volume = "5", number = "3", pages = "29:1--29:??", month = jul, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1541885.1541890", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:27 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We provide efficient constant-factor approximation algorithms for the problems of finding a hierarchical clustering of a point set in any metric space, minimizing the sum of minimimum spanning tree lengths within each cluster, and in the hyperbolic or Euclidean planes, minimizing the sum of cluster perimeters. Our algorithms for the hyperbolic and Euclidean planes can also be used to provide a pants decomposition, that is, a set of disjoint simple closed curves partitioning the plane minus the input points into subsets with exactly three boundary components, with approximately minimum total length. In the Euclidean case, these curves are squares; in the hyperbolic case, they combine our Euclidean square pants decomposition with our tree clustering method for general metric spaces.", acknowledgement = ack-nhfb, articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Demaine:2009:MM, author = "Erik D. Demaine and Mohammadtaghi Hajiaghayi and Hamid Mahini and Amin S. Sayedi-Roshkhar and Shayan Oveisgharan and Morteza Zadimoghaddam", title = "Minimizing movement", journal = j-TALG, volume = "5", number = "3", pages = "30:1--30:??", month = jul, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1541885.1541891", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:27 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give approximation algorithms and inapproximability results for a class of movement problems. In general, these problems involve planning the coordinated motion of a large collection of objects (representing anything from a robot swarm or firefighter team to map labels or network messages) to achieve a global property of the network while minimizing the maximum or average movement. In particular, we consider the goals of achieving connectivity (undirected and directed), achieving connectivity between a given pair of vertices, achieving independence (a dispersion problem), and achieving a perfect matching (with applications to multicasting). This general family of movement problems encompasses an intriguing range of graph and geometric algorithms, with several real-world applications and a surprising range of approximability. In some cases, we obtain tight approximation and inapproximability results using direct techniques (without use of PCP), assuming just that P $ \neq $ NP.", acknowledgement = ack-nhfb, articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Borradaile:2009:ASS, author = "Glencora Borradaile and Philip Klein and Claire Mathieu", title = "An {$ {O}(n \log n) $} approximation scheme for {Steiner} tree in planar graphs", journal = j-TALG, volume = "5", number = "3", pages = "31:1--31:??", month = jul, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1541885.1541892", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Mar 16 09:37:25 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Borradaile:2009:LAS, author = "Glencora Borradaile and Philip Klein and Claire Mathieu", title = "An {$ O(n \log n) $} approximation scheme for {Steiner} tree in planar graphs", journal = j-TALG, volume = "5", number = "3", pages = "31:1--31:??", month = jul, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1541885.1541892", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:27 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give a Polynomial-Time Approximation Scheme (PTAS) for the Steiner tree problem in planar graphs. The running time is {$ O(n \log n) $}.", acknowledgement = ack-nhfb, articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Charikar:2009:NOA, author = "Moses Charikar and Konstantin Makarychev and Yury Makarychev", title = "Near-optimal algorithms for maximum constraint satisfaction problems", journal = j-TALG, volume = "5", number = "3", pages = "32:1--32:??", month = jul, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1541885.1541893", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:27 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we present two approximation algorithms for the maximum constraint satisfaction problem with $k$ variables in each constraint (MAX $k$-CSP). Given a $ (1 - \epsilon) $ satisfiable 2CSP our first algorithm finds an assignment of variables satisfying a {$ 1 - O(\sqrt \epsilon) $} fraction of all constraints. The best previously known result, due to Zwick, was {$ 1 - O(\epsilon^{1 / 3}) $}. The second algorithm finds a {$ c k / 2^k $} approximation for the MAX {$k$}-CSP problem (where {$ c > 0.44 $} is an absolute constant). This result improves the previously best known algorithm by Hast, which had an approximation guarantee of {$ \Omega (k / (2^k \log k)) $}. Both results are optimal assuming the unique games conjecture and are based on rounding natural semidefinite programming relaxations. We also believe that our algorithms and their analysis are simpler than those previously known.", acknowledgement = ack-nhfb, articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Andrews:2009:IFP, author = "Matthew Andrews", title = "Instability of {FIFO} in the permanent sessions model at arbitrarily small network loads", journal = j-TALG, volume = "5", number = "3", pages = "33:1--33:??", month = jul, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1541885.1541894", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:27 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show that for any $ r > 0 $, there is a network of First-In-First-Out servers and a fixed set of sessions such that:\par --- The network load is $r$ with respect to the permanent sessions model with bounded arrivals.\par --- The network can be made unstable.", acknowledgement = ack-nhfb, articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Golubchik:2009:AAD, author = "Leana Golubchik and Sanjeev Khanna and Samir Khuller and Ramakrishna Thurimella and An Zhu", title = "Approximation algorithms for data placement on parallel disks", journal = j-TALG, volume = "5", number = "4", pages = "34:1--34:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597037", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study an optimization problem that arises in the context of data placement in a multimedia storage system. We are given a collection of {$M$} multimedia objects (data objects) that need to be assigned to a storage system consisting of {$N$} disks {$ d_1 $}, {$ d_2 $}, \ldots {}, {$ d_N $}. We are also given sets {$ U_1 $}, {$ U_2 $}, \ldots {}, {$ U_M $} such that {$ U_i $} is the set of clients seeking the {$i$} th data object. Each disk {$ d_j $} is characterized by two parameters, namely, its storage capacity {$ C_j $} which indicates the maximum number of data objects that may be assigned to it, and a load capacity {$ L_j $} which indicates the maximum number of clients that it can serve. The goal is to find a placement of data objects to disks and an assignment of clients to disks so as to maximize the total number of clients served, subject to the capacity constraints of the storage system. We study this data placement problem for two natural classes of storage systems, namely, homogeneous and uniform ratio. We show that an algorithm developed by Shachnai and Tamir [2000a] for data placement achieves the best possible absolute bound regarding the number of clients that can always be satisfied. We also show how to implement the algorithm so that it has a running time of {$ O((N + M) \log (N + M)) $}. In addition, we design a polynomial-time approximation scheme, solving an open problem posed in the same paper.", acknowledgement = ack-nhfb, articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Guha:2009:SEE, author = "Sudipto Guha and Andrew McGregor and Suresh Venkatasubramanian", title = "Sublinear estimation of entropy and information distances", journal = j-TALG, volume = "5", number = "4", pages = "35:1--35:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597038", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In many data mining and machine learning problems, the data items that need to be clustered or classified are not arbitrary points in a high-dimensional space, but are distributions, that is, points on a high-dimensional simplex. For distributions, natural measures are not l$_p$ distances, but information-theoretic measures such as the Kullback--Leibler and Hellinger divergences. Similarly, quantities such as the entropy of a distribution are more natural than frequency moments. Efficient estimation of these quantities is a key component in algorithms for manipulating distributions. Since the datasets involved are typically massive, these algorithms need to have only sublinear complexity in order to be feasible in practice. We present a range of sublinear-time algorithms in various oracle models in which the algorithm accesses the data via an oracle that supports various queries. In particular, we answer a question posed by Batu et al. on testing whether two distributions are close in an information-theoretic sense given independent samples. We then present optimal algorithms for estimating various information-divergences and entropy with a more powerful oracle called the combined oracle that was also considered by Batu et al. Finally, we consider sublinear-space algorithms for these quantities in the data-stream model. In the course of doing so, we explore the relationship between the aforementioned oracle models and the data-stream model. This continues work initiated by Feigenbaum et al. An important additional component to the study is considering data streams that are ordered randomly rather than just those which are ordered adversarially.", acknowledgement = ack-nhfb, articleno = "35", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Levin:2009:GMC, author = "Asaf Levin", title = "A generalized minimum cost $k$-clustering", journal = j-TALG, volume = "5", number = "4", pages = "36:1--36:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597039", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problems of set partitioning into $k$ clusters with minimum total cost and minimum of the maximum cost of a cluster. The cost function is given by an oracle, and we assume that it satisfies some natural structural constraints. That is, we assume that the cost function is monotone, the cost of a singleton is zero, and we assume that for all {$ S \cap S' \neq \oslash $} the following holds {$ c(S) + c(S') \geq c(S \cup S') $}. For the problem of minimizing the maximum cost of a cluster we present a {$ (2 k - 1) $}-approximation algorithm for {$ k \geq 3 $}, a 2-approximation algorithm for {$ k = 2 $}, and we also show a lower bound of $k$ on the performance guarantee of any polynomial-time algorithm. For the problem of minimizing the total cost of all the clusters, we present a 2-approximation algorithm for the case where $k$ is a fixed constant, a $ (4 k - 3) $-approximation where $k$ is unbounded, and we show a lower bound of $2$ on the approximation ratio of any polynomial-time algorithm. Our lower bounds do not depend on the common assumption that P $ \neq $ NP.", acknowledgement = ack-nhfb, articleno = "36", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Farach-Colton:2009:BHO, author = "Martin Farach-Colton and Rohan J. Fernandes and Miguel A. Mosteiro", title = "Bootstrapping a hop-optimal network in the weak sensor model", journal = j-TALG, volume = "5", number = "4", pages = "37:1--37:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597040", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Sensor nodes are very weak computers that get distributed at random on a surface. Once deployed, they must wake up and form a radio network. Sensor network bootstrapping research thus has three parts: One must model the restrictions on sensor nodes; one must prove that the connectivity graph of the sensors has a subgraph that would make a good network; and one must give a distributed protocol for finding such a network subgraph that can be implemented on sensor nodes. Although many particular restrictions on sensor nodes are implicit or explicit in many papers, there remain many inconsistencies and ambiguities from paper to paper. The lack of a clear model means that solutions to the network bootstrapping problem in both the theory and systems literature all violate constraints on sensor nodes. For example, random geometric graph results on sensor networks predict the existence of subgraphs on the connectivity graph with good route-stretch, but these results do not address the degree of such a graph, and sensor networks must have constant degree. Furthermore, proposed protocols for actually finding such graphs require that nodes have too much memory, whereas others assume the existence of a contention-resolution mechanism. We present a formal Weak Sensor model that summarizes the literature on sensor node restrictions, taking the most restrictive choices when possible. We show that sensor connectivity graphs have low-degree subgraphs with good hop-stretch, as required by the Weak Sensor model. Finally, we give a Weak Sensor model-compatible protocol for finding such graphs. Ours is the first network initialization algorithm that is implementable on sensor nodes.", acknowledgement = ack-nhfb, articleno = "37", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Eppstein:2009:AMI, author = "David Eppstein", title = "All maximal independent sets and dynamic dominance for sparse graphs", journal = j-TALG, volume = "5", number = "4", pages = "38:1--38:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597042", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We describe algorithms, based on Avis and Fukuda's reverse search paradigm, for listing all maximal independent sets in a sparse graph in polynomial time and delay per output. For bounded degree graphs, our algorithms take constant time per set generated; for minor-closed graph families, the time is {$ O(n) $} per set, and for more general sparse graph families we achieve subquadratic time per set. We also describe new data structures for maintaining a dynamic vertex set {$S$} in a sparse or minor-closed graph family, and querying the number of vertices not dominated by {$S$}; for minor-closed graph families the time per update is constant, while it is sublinear for any sparse graph family. We can also maintain a dynamic vertex set in an arbitrary {$m$}-edge graph and test the independence of the maintained set in time {$ O(\sqrt m) $} per update. We use the domination data structures as part of our enumeration algorithms.", acknowledgement = ack-nhfb, articleno = "38", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Reed:2009:LTA, author = "Bruce Reed and David R. Wood", title = "A linear-time algorithm to find a separator in a graph excluding a minor", journal = j-TALG, volume = "5", number = "4", pages = "39:1--39:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597043", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Let {$G$} be an {$n$}-vertex {$m$}-edge graph with weighted vertices. A pair of vertex sets {$ A, B \subseteq V(G) $} is a {$ 2 / 3 $}-separation of order {$ |A \cap B| $} if {$ A \cup B = V(G) $}, there is no edge between {$A$}--{$B$} and {$B$}--{$A$}, and both {$A$}--{$B$} and {$B$}--{$A$} have weight at most {$ 2 / 3 $} the total weight of {$G$}. Let {$ l \in Z^+ $} be fixed. Alon et al. [1990] presented an algorithm that in {$ O(n^{1 / 2m}) $} time, outputs either a {$ K_l $}-minor of {$G$}, or a separation of {$G$} of order {$ O(n^{1 / 2}) $}. Whether there is a {$ O(n + m) $}-time algorithm for this theorem was left as an open problem. In this article, we obtain a {$ O(n + m) $}-time algorithm at the expense of a {$ O(n^{2 / 3}) $} separator. Moreover, our algorithm exhibits a trade-off between time complexity and the order of the separator. In particular, for any given {$ \epsilon \in [0, 1 / 2] $}, our algorithm outputs either a {$ K_l $}-minor of {$G$}, or a separation of {$G$} with order {$ O(n^{(2 - \epsilon) / 3}) $} in {$ O(n^{1 + \epsilon } + m) $} time. As an application we give a fast approximation algorithm for finding an independent set in a graph with no {$ K_l $}-minor.", acknowledgement = ack-nhfb, articleno = "39", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ito:2009:EIC, author = "Hiro Ito and Kazuo Iwama", title = "Enumeration of isolated cliques and pseudo-cliques", journal = j-TALG, volume = "5", number = "4", pages = "40:1--40:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597044", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we consider isolated cliques and isolated dense subgraphs. For a given graph {$G$}, a vertex subset {$S$} of size {$k$} (and also its induced subgraph {$ G(S) $}) is said to be {$c$}-isolated if {$G$} (S) is connected to its outside via less than {$ c k $} edges. The number {$c$} is sometimes called the isolation factor. The subgraph appears more isolated if the isolation factor is smaller. The main result in this work shows that for a fixed constant {$c$}, we can enumerate all $c$-isolated maximal cliques (including a maximum one, if any) in linear time. In more detail, we show that, for a given graph {$G$} of {$n$} vertices and {$m$} edges, and a positive real number {$c$}, all $c$-isolated maximal cliques can be enumerated in time {$ O(c^4 2^{2c} m) $}. From this, we can see that: (1) if {$c$} is a constant, all {$c$}-isolated maximal cliques can be enumerated in linear time, and (2) if {$ c = O(\log n) $}, all {$c$}-isolated maximal cliques can be enumerated in polynomial time. Moreover, we show that these bounds are tight. That is, if {$ f(n) $} is an increasing function not bounded by any constant, then there is a graph of {$n$} vertices and $m$ edges for which the number of $ f(n) $-isolated maximal cliques is superlinear in $ n + m $. Furthermore, if $ f(n) = \omega (\log n) $, there is a graph of $n$ vertices and $m$ edges for which the number of $ f(n) $-isolated maximal cliques is superpolynomial in $ n + m $. We next introduce the idea of pseudo-cliques. A pseudo-clique having an average degree $ \alpha $ and a minimum degree $ \beta $, denoted by {$ {\rm PC}(\alpha, \beta) $}, is a set {$ V' \subseteq V $} such that the subgraph induced by {$ V' $} has an average degree of at least {$ \alpha $} and a minimum degree of at least {$ \beta $}. This article investigates these, and obtains some cases that can be solved in polynomial time and some other cases that have a superpolynomial number of solutions. Especially, we show the following results, where {$k$} is the number of vertices of the isolated pseudo-cliques: (1) For any $ \epsilon > 0 $ there is a graph of $n$ vertices for which the number of $1$-isolated {$ {\rm PC}(k - (\log k)^{1 + \epsilon }, k / (\log k)^{1 + \epsilon }) $} is superpolynomial, and (2) there is a polynomial-time algorithm which enumerates all {$c$}-isolated {$ {\rm PC}(k - \log k, k / \log k) $}, for any constant {$c$}.", acknowledgement = ack-nhfb, articleno = "40", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Karakostas:2009:BAR, author = "George Karakostas", title = "A better approximation ratio for the vertex cover problem", journal = j-TALG, volume = "5", number = "4", pages = "41:1--41:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597045", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We reduce the approximation factor for the vertex cover to {$ 2 - \Theta (1 / \sqrt {\log n}) $} (instead of the previous {$ 2 - \Theta (\ln \ln n / 2 \ln n) $} obtained by Bar-Yehuda and Even [1985] and Monien and Speckenmeyer [1985]). The improvement of the vanishing factor comes as an application of the recent results of Arora et al. [2004] that improved the approximation factor of the sparsest cut and balanced cut problems. In particular, we use the existence of two big and well-separated sets of nodes in the solution of the semidefinite relaxation for balanced cut, proven by Arora et al. [2004]. We observe that a solution of the semidefinite relaxation for vertex cover, when strengthened with the triangle inequalities, can be transformed into a solution of a balanced cut problem, and therefore the existence of big well-separated sets in the sense of Arora et al. [2004] translates into the existence of a big independent set.", acknowledgement = ack-nhfb, articleno = "41", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Berend:2009:LAC, author = "Daniel Berend and Vladimir Braverman", title = "A linear algorithm for computing convex hulls for random lines", journal = j-TALG, volume = "5", number = "4", pages = "42:1--42:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597046", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Finding the convex hull of $n$ points in the plane requires {$ O(n \log n) $} time in general. In Devroye and Toussaint [1993] and Golin et al. [2002] the problem of computing the convex hull of the intersection points of {$n$} lines was considered, where the lines are chosen randomly according to two various models. In both models, linear-time algorithms were developed. Here we improve the results of Devroye and Toussaint [1993] by giving a universal algorithm for a wider range of distributions.", acknowledgement = ack-nhfb, articleno = "42", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Kao:2009:RFD, author = "Ming-Yang Kao and Manan Sanghi and Robert Schweller", title = "Randomized fast design of short {DNA} words", journal = j-TALG, volume = "5", number = "4", pages = "43:1--43:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597047", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problem of efficiently designing sets (codes) of equal-length DNA strings (words) that satisfy certain combinatorial constraints. This problem has numerous motivations including DNA self-assembly and DNA computing. Previous work has extended results from coding theory to obtain bounds on code size for new biologically motivated constraints and has applied heuristic local search and genetic algorithm techniques for code design. This article proposes a natural optimization formulation of the DNA code design problem in which the goal is to design $n$ strings that satisfy a given set of constraints while minimizing the length of the strings. For multiple sets of constraints, we provide simple randomized algorithms that run in time polynomial in $n$ and any given constraint parameters, and output strings of length within a constant factor of the optimal with high probability. To the best of our knowledge, this work is the first to consider this type of optimization problem in the context of DNA code design.", acknowledgement = ack-nhfb, articleno = "43", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Fernandez-Baca:2009:PAU, author = "David Fern{\'a}ndez-Baca and Balaji Venkatachalam", title = "Parametric analysis for ungapped {Markov} models of evolution", journal = j-TALG, volume = "5", number = "4", pages = "44:1--44:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597048", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Efficient sensitivity analysis algorithms are presented for two problems arising in the study of Markov models of sequence evolution: ancestral reconstruction in evolutionary trees and local ungapped alignment under log-odds scoring. The algorithms generate complete descriptions of the optimum solutions for all possible values of the evolutionary distance. The running time for the parametric ancestral reconstruction problem under the Kimura 2-parameter model is {$ O(k n + k n^{2 / 3} \log k) $}, where {$n$} is the number of sequences and {$k$} is their length, assuming all edges have the same length. For the parametric gapless alignment problem under the Jukes-Cantor model, the running time is {$ O(m n + m n^{2 / 3} \log m) $}, where {$m$} and {$n$} are the sequence lengths and {$ n \leq m $}.", acknowledgement = ack-nhfb, articleno = "44", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Scott:2009:PCS, author = "Alexander D. Scott and Gregory B. Sorkin", title = "{Polynomial} constraint satisfaction problems, graph bisection, and the {Ising} partition function", journal = j-TALG, volume = "5", number = "4", pages = "45:1--45:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597049", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP. Where the usual CSPs from computer science and optimization have real-valued score functions, and partition functions from physics have monomials, PCSP has scores that are arbitrary multivariate formal polynomials, or indeed take values in an arbitrary ring. Although PCSP is much more general than CSP, remarkably, all (exact, exponential-time) algorithms we know of for 2-CSP (where each score depends on at most 2 variables) extend to 2-PCSP, at the expense of just a polynomial factor in running time. Specifically, we extend the reduction-based algorithm of Scott and Sorkin [2007]; the specialization of that approach to sparse random instances, where the algorithm runs in polynomial expected time; dynamic-programming algorithms based on tree decompositions; and the split-and-list matrix-multiplication algorithm of Williams [2004]. This gives the first polynomial-space exact algorithm more efficient than exhaustive enumeration for the well-studied problems of finding a maximum bisection of a graph, and calculating the partition function of an Ising model. It also yields the most efficient algorithm known for certain instances of counting and/or weighted Maximum Independent Set. Furthermore, PCSP solves both optimization and counting versions of a wide range of problems, including all CSPs, and thus enables samplers including uniform sampling of optimal solutions and Gibbs sampling of all solutions.", acknowledgement = ack-nhfb, articleno = "45", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Nguyen:2009:LDL, author = "Phong Q. Nguyen and Damien Stehl{\'e}", title = "Low-dimensional lattice basis reduction revisited", journal = j-TALG, volume = "5", number = "4", pages = "46:1--46:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597050", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Lattice reduction is a geometric generalization of the problem of computing greatest common divisors. Most of the interesting algorithmic problems related to lattice reduction are NP-hard as the lattice dimension increases. This article deals with the low-dimensional case. We study a greedy lattice basis reduction algorithm for the Euclidean norm, which is arguably the most natural lattice basis reduction algorithm because it is a straightforward generalization of an old two-dimensional algorithm of Lagrange, usually known as Gauss' algorithm, and which is very similar to Euclid's gcd algorithm. Our results are twofold. From a mathematical point of view, we show that up to dimension four, the output of the greedy algorithm is optimal: The output basis reaches all the successive minima of the lattice. However, as soon as the lattice dimension is strictly higher than four, the output basis may be arbitrarily bad as it may not even reach the first minimum. More importantly, from a computational point of view, we show that up to dimension four, the bit-complexity of the greedy algorithm is quadratic without fast integer arithmetic, just like Euclid's gcd algorithm. This was already proved by Semaev up to dimension three using rather technical means, but it was previously unknown whether or not the algorithm was still polynomial in dimension four. We propose two different analyzes: a global approach based on the geometry of the current basis when the length decrease stalls, and a local approach showing directly that a significant length decrease must occur every {$ O(1) $} consecutive steps. Our analyzes simplify Semaev's analysis in dimensions two and three, and unify the cases of dimensions two to four. Although the global approach is much simpler, we also present the local approach because it gives further information on the behavior of the algorithm.", acknowledgement = ack-nhfb, articleno = "46", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Finocchi:2009:RD, author = "Irene Finocchi and Fabrizio Grandoni and Giuseppe F. Italiano", title = "Resilient dictionaries", journal = j-TALG, volume = "6", number = "1", pages = "1:1--1:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644016", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We address the problem of designing data structures in the presence of faults that may arbitrarily corrupt memory locations. More precisely, we assume that an adaptive adversary can arbitrarily overwrite the content of up to $ \delta $ memory locations, that corrupted locations cannot be detected, and that only {$ O(1) $} memory locations are safe. In this framework, we call a data structure resilient if it is able to operate correctly (at least) on the set of uncorrupted values. We present a resilient dictionary, implementing search, insert, and delete operations. Our dictionary has {$ O(\log n + \delta) $} expected amortized time per operation, and {$ O(n) $} space complexity, where {$n$} denotes the current number of keys in the dictionary. We also describe a deterministic resilient dictionary, with the same amortized cost per operation over a sequence of at least {$ \delta^\epsilon $} operations, where {$ \epsilon > 0 $} is an arbitrary constant. Finally, we show that any resilient comparison-based dictionary must take {$ \Omega (\log n + \delta) $} expected time per search. Our results are achieved by means of simple, new techniques which might be of independent interest for the design of other resilient algorithms.", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Demaine:2009:ODA, author = "Erik D. Demaine and Shay Mozes and Benjamin Rossman and Oren Weimann", title = "An optimal decomposition algorithm for tree edit distance", journal = j-TALG, volume = "6", number = "1", pages = "2:1--2:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644017", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The edit distance between two ordered rooted trees with vertex labels is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling existing nodes, as well as inserting new nodes. In this article, we present a worst-case {$ O(n^3) $}-time algorithm for the problem when the two trees have size {$n$}, improving the previous best {$ O(n^3 \log n) $}-time algorithm. Our result requires a novel adaptive strategy for deciding how a dynamic program divides into subproblems, together with a deeper understanding of the previous algorithms for the problem. We prove the optimality of our algorithm among the family of decomposition strategy algorithms-which also includes the previous fastest algorithms-by tightening the known lower bound of {$ \Omega (n^2 \log^2 n) $} to {$ \Omega (n^3) $}, matching our algorithm's running time. Furthermore, we obtain matching upper and lower bounds for decomposition strategy algorithms of {$ \Theta (n m^2 (1 + \log n / m)) $} when the two trees have sizes {$m$} and {$n$} and {$ m < n $}.", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bille:2009:IAS, author = "Philip Bille and Rolf Fagerberg and Inge Li G{\o}rtz", title = "Improved approximate string matching and regular expression matching on {Ziv--Lempel} compressed texts", journal = j-TALG, volume = "6", number = "1", pages = "3:1--3:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644018", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the approximate string matching and regular expression matching problem for the case when the text to be searched is compressed with the Ziv--Lempel adaptive dictionary compression schemes. We present a time-space trade-off that leads to algorithms improving the previously known complexities for both problems. In particular, we significantly improve the space bounds, which in practical applications are likely to be a bottleneck.", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Duch:2009:URK, author = "Amalia Duch and Conrado Mart{\'\i}nez", title = "Updating relaxed {$ {K} $}-d trees", journal = j-TALG, volume = "6", number = "1", pages = "4:1--4:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644019", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this work we present an in-depth study of randomized relaxed $k$--$d$ trees. It covers two fundamental aspects: the randomized algorithms that allow to preserve the random properties of relaxed $k$--$d$ trees and the mathematical analysis of the expected performance of these algorithms. In particular, we describe randomized update algorithms for $k$--$d$ trees based on the split and join algorithms of Duch et al. [1998]. We carry out an analysis of the expected cost of all these algorithms, using analytic combinatorics techniques. We show that the average cost of split and join is of the form {$ \zeta (K) \cdot n^{\phi (K)} + o(n^{\phi (K)}) $}, with {$ 1 \leq \phi (K) < 1.561552813 $}, and we give explicit formul{\ae} for both {$ \zeta (K) $} and {$ \phi (K) $}. These results on the average performance of split and join imply that the expected cost of an insertion or a deletion is {$ \Theta (n^{\phi (K) - 1}) $} when {$ K > 2 $} and {$ \Theta (\log n) $} for {$ K = 2 $}.", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Nutov:2009:ACA, author = "Zeev Nutov", title = "Approximating connectivity augmentation problems", journal = j-TALG, volume = "6", number = "1", pages = "5:1--5:19", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644020", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Let {$ G = (V, E) $} be an undirected graph and let {$ S \subseteq V $}. The {$S$}-connectivity {$ \lambda^S_G(u, v) $} of a node pair {$ (u, v) $} in {$G$} is the maximum number of {$ u v $}-paths that no two of them have an edge or a node in {$ S - \{ u, v \} $} in common. The corresponding Connectivity Augmentation (CA) problem is: given a graph {$ G = (V, E) $}, a node subset {$ S \subseteq V $}, and a nonnegative integer requirement function {$ r(u, v) $} on {$ V \times V $}, add a minimum size set F of new edges to {$G$} so that {$ \lambda^S_{G + F}(u, v) \geq r(u, v) $} for all {$ (u, v) \in V \times V $}. Three extensively studied particular cases are: the Edge-CA ({$ S = \oslash $}), the Node-CA ({$ S = V $}), and the Element-CA {$ r(u, v) = 0 $} whenever {$ u \in S $} or {$ v \in S $}. A polynomial-time algorithm for Edge-CA was developed by Frank. In this article we consider the Element-CA and the Node-CA, that are NP-hard even for {$ r(u, v) \in \{ 0, 2 \} $}. The best known ratios for these problems were: 2 for Element-CA and {$ O(r_{\rm max} \cdot \ln n) $} for Node-CA, where {$ r_{\rm max} = \max_{u,_v} \in V r(u, v) $} and {$ n = |V| $}. Our main result is a 7/4-approximation algorithm for the Element-CA, improving the previously best known 2-approximation. For Element-CA with {$ r(u, v) \in \{ 0, 1, 2 \} $} we give a {$ 3 / 2 $}-approximation algorithm. These approximation ratios are based on a new splitting-off theorem, which implies an improved lower bound on the number of edges needed to cover a skew-supermodular set function. For Node-CA we establish the following approximation threshold: Node-CA with {$ r(u, v) \in \{ 0, k \} $} cannot be approximated within {$ O(2^{\log^{1 - \epsilon } n}) $} for any fixed {$ \epsilon > 0 $}, unless NP {$ \subseteq $} DTIME({$ n^{\polylog (n)} $} ).", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Demetrescu:2009:TSP, author = "Camil Demetrescu and Irene Finocchi and Andrea Ribichini", title = "Trading off space for passes in graph streaming problems", journal = j-TALG, volume = "6", number = "1", pages = "6:1--6:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644021", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Data stream processing has recently received increasing attention as a computational paradigm for dealing with massive data sets. Surprisingly, no algorithm with both sublinear space and passes is known for natural graph problems in classical read-only streaming. Motivated by technological factors of modern storage systems, some authors have recently started to investigate the computational power of less restrictive models where writing streams is allowed. In this article, we show that the use of intermediate temporary streams is powerful enough to provide effective space-passes tradeoffs for natural graph problems. In particular, for any space restriction of $s$ bits, we show that single-source shortest paths in directed graphs with small positive integer edge weights can be solved in {$ O((n \log^{3 / 2} n) / \sqrt s) $} passes. The result can be generalized to deal with multiple sources within the same bounds. This is the first known streaming algorithm for shortest paths in directed graphs. For undirected connectivity, we devise an {$ O((n \log n) / s) $} passes algorithm. Both problems require {$ \Omega (n / s) $} passes under the restrictions we consider. We also show that the model where intermediate temporary streams are allowed can be strictly more powerful than classical streaming for some problems, while maintaining all of its hardness for others.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Pettie:2009:LDS, author = "Seth Pettie", title = "{Low} distortion spanners", journal = j-TALG, volume = "6", number = "1", pages = "7:1--7:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644022", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A spanner of an undirected unweighted graph is a subgraph that approximates the distance metric of the original graph with some specified accuracy. Specifically, we say {$ H \subseteq G $} is an {$f$}-spanner of {$G$} if any two vertices {$ u, v $} at distance {$d$} in {$G$} are at distance at most {$ f(d) $} in {$H$}. There is clearly some trade-off between the sparsity of {$H$} and the distortion function {$f$}, though the nature of the optimal trade-off is still poorly understood. In this article we present a simple, modular framework for constructing sparse spanners that is based on interchangeable components called connection schemes. By assembling connection schemes in different ways we can recreate the additive 2- and 6-spanners of Aingworth et al. [1999] and Baswana et al. [2009], and give spanners whose multiplicative distortion quickly tends toward 1. Our results rival the simplicity of all previous algorithms and provide substantial improvements (up to a doubly exponential reduction in edge density) over the comparable spanners of Elkin and Peleg [2004] and Thorup and Zwick [2006].", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Mehlhorn:2009:MCB, author = "Kurt Mehlhorn and Dimitrios Michail", title = "Minimum cycle bases: {Faster} and simpler", journal = j-TALG, volume = "6", number = "1", pages = "8:1--8:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644023", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problem of computing exact or approximate minimum cycle bases of an undirected (or directed) graph {$G$} with {$m$} edges, {$n$} vertices and nonnegative edge weights. In this problem, a {$ \{ 0, 1 \} ( - 1, 0, 1) $} incidence vector is associated with each cycle and the vector space over {$ F_2 (Q) $} generated by these vectors is the cycle space of {$G$}. A set of cycles is called a cycle basis of {$G$} if it forms a basis for its cycle space. A cycle basis where the sum of the weights of the cycles is minimum is called a minimum cycle basis of {$G$}. Cycle bases of low weight are useful in a number of contexts, for example, the analysis of electrical networks, structural engineering, chemistry, and surface reconstruction. There exists a set of {$ \Theta (m n) $} cycles which is guaranteed to contain a minimum cycle basis. A minimum basis can be extracted by Gaussian elimination. The resulting algorithm [Horton 1987] was the first polynomial-time algorithm. Faster and more complicated algorithms have been found since then. We present a very simple method for extracting a minimum cycle basis from the candidate set with running time {$ O(m^2 n) $}, which improves the running time for sparse graphs. Furthermore, in the undirected case by using bit-packing we improve the running time also in the case of dense graphs. For undirected graphs we derive an {$ O(m^2 n / \log n + n^2 m) $} algorithm. For directed graphs we get an {$ O(m^3 n) $} deterministic and an {$ O(m^2 n) $} randomized algorithm. Our results improve the running times of both exact and approximate algorithms. Finally, we derive a smaller candidate set with size in {$ \Omega (m) \cap O(m n) $}.", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gaspers:2009:ETA, author = "Serge Gaspers and Dieter Kratsch and Mathieu Liedloff and Ioan Todinca", title = "Exponential time algorithms for the minimum dominating set problem on some graph classes", journal = j-TALG, volume = "6", number = "1", pages = "9:1--9:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644024", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The minimum dominating set problem remains NP-hard when restricted to any of the following graph classes: $c$-dense graphs, chordal graphs, 4-chordal graphs, weakly chordal graphs, and circle graphs. Developing and using a general approach, for each of these graph classes we present an exponential time algorithm solving the minimum dominating set problem faster than the best known algorithm for general graphs. Our algorithms have the following running time: {$ O(1.4124^n) $} for chordal graphs, {$ O(1.4776^n) $} for weakly chordal graphs, {$ O(1.4845^n) $} for 4-chordal graphs, {$ O(1.4887^n) $} for circle graphs, and {$ O(1.2273^{(1 + \sqrt {1 - 2 c}) n}) $} for {$c$}-dense graphs.", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chan:2009:OTE, author = "Ho-Leung Chan and Joseph Wun-Tat Chan and Tak-Wah Lam and Lap-Kei Lee and Kin-Sum Mak and Prudence W. H. Wong", title = "Optimizing throughput and energy in online deadline scheduling", journal = j-TALG, volume = "6", number = "1", pages = "10:1--10:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644025", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article extends the study of online algorithms for energy-efficient deadline scheduling to the overloaded setting. Specifically, we consider a processor that can vary its speed between $0$ and a maximum speed {$T$} to minimize its energy usage (the rate is believed to be a cubic function of the speed). As the speed is upper bounded, the processor may be overloaded with jobs and no scheduling algorithms can guarantee to meet the deadlines of all jobs. An optimal schedule is expected to maximize the throughput, and furthermore, its energy usage should be the smallest among all schedules that achieve the maximum throughput. In designing a scheduling algorithm, one has to face the dilemma of selecting more jobs and being conservative in energy usage. If we ignore energy usage, the best possible online algorithm is 4-competitive on throughput [Koren and Shasha 1995]. On the other hand, existing work on energy-efficient scheduling focuses on a setting where the processor speed is unbounded and the concern is on minimizing the energy to complete all jobs; {$ O(1) $}-competitive online algorithms with respect to energy usage have been known [Yao et al. 1995; Bansal et al. 2007a; Li et al. 2006]. This article presents the first online algorithm for the more realistic setting where processor speed is bounded and the system may be overloaded; the algorithm is {$ O(1) $}-competitive on both throughput and energy usage. If the maximum speed of the online scheduler is relaxed slightly to {$ (1 + \epsilon) T $} for some {$ \epsilon > 0 $}, we can improve the competitive ratio on throughput to arbitrarily close to one, while maintaining {$ O(1) $}-competitiveness on energy usage.", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Alon:2009:ACM, author = "Noga Alon and Yossi Azar and Shai Gutner", title = "Admission control to minimize rejections and online set cover with repetitions", journal = j-TALG, volume = "6", number = "1", pages = "11:1--11:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644026", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the admission control problem in general networks. Communication requests arrive over time, and the online algorithm accepts or rejects each request while maintaining the capacity limitations of the network. The admission control problem has been usually analyzed as a benefit problem, where the goal is to devise an online algorithm that accepts the maximum number of requests possible. The problem with this objective function is that even algorithms with optimal competitive ratios may reject almost all of the requests, when it would have been possible to reject only a few. This could be inappropriate for settings in which rejections are intended to be rare events. In this article, we consider preemptive online algorithms whose goal is to minimize the number of rejected requests. Each request arrives together with the path it should be routed on. We show an {$ O(\log^2 (m c)) $}-competitive randomized algorithm for the weighted case, where {$m$} is the number of edges in the graph and {$c$} is the maximum edge capacity. For the unweighted case, we give an {$ O(\log m \log c) $}-competitive randomized algorithm. This settles an open question of Blum et al. [2001]. We note that allowing preemption and handling requests with given paths are essential for avoiding trivial lower bounds. The admission control problem is a generalization of the online set cover with repetitions problem, whose input is a family of {$m$} subsets of a ground set of {$n$} elements. Elements of the ground set are given to the online algorithm one by one, possibly requesting each element a multiple number of times. (If each element arrives at most once, this corresponds to the online set cover problem.) The algorithm must cover each element by different subsets, according to the number of times it has been requested. We give an {$ O(\log m \log n) $}-competitive randomized algorithm for the online set cover with repetitions problem. This matches a recent lower bound of {$ \Omega (\log m \log n) $} given by Korman [2005] (based on Feige [1998]) for the competitive ratio of any randomized polynomial time algorithm, under the BPP /= NP assumption. Given any constant {$ \epsilon > 0 $}, an {$ O(\log m \log n) $}-competitive deterministic bicriteria algorithm is shown that covers each element by at least {$ (1 - \epsilon) k $} sets, where {$k$} is the number of times the element is covered by the optimal solution.", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hay:2009:JRM, author = "David Hay and Gabriel Scalosub", title = "Jitter regulation for multiple streams", journal = j-TALG, volume = "6", number = "1", pages = "12:1--12:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644027", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "For widely used interactive communication, it is essential that traffic is kept as smooth as possible; the smoothness of the traffic is typically captured by its delay jitter, that is, the difference between the maximal and minimal end-to-end delays. The task of minimizing the jitter is done by jitter regulators that use a limited-size buffer in order to shape the traffic. In many real-life situations regulators must handle multiple streams simultaneously and provide low jitter on each of them separately. Moreover, communication links have limited capacity, and these may pose further restrictions on the choices made by the regulator. This article investigates the problem of minimizing jitter in such an environment, using a fixed-size buffer. We show that the offline version of the problem can be solved in polynomial time, by introducing an efficient offline algorithm that finds a release schedule with optimal jitter. When regulating {$M$} streams in the online setting, we take a competitive analysis point of view and note that, in the upcapacitated case, previous results in Mansour and Patt-Shamir [2001] can be extended to an online algorithm that uses a buffer of size {$ 2 \cdot M \cdot B $} and obtains the optimal jitter possible with a buffer of size {$B$} (and an offline algorithm). The question arises whether such a resource augmentation is essential. We answer this question in the affirmative, by proving a lower bound that is tight up to a factor of 2, thus showing that jitter regulation does not scale well as the number of streams increases unless the buffer is sized-up proportionally.", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Becchetti:2009:LCA, author = "Luca Becchetti and Alberto Marchetti-Spaccamela and Andrea Vitaletti and Peter Korteweg and Martin Skutella and Leen Stougie", title = "Latency-constrained aggregation in sensor networks", journal = j-TALG, volume = "6", number = "1", pages = "13:1--13:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644028", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A sensor network consists of sensing devices which may exchange data through wireless communication; sensor networks are highly energy constrained since they are usually battery operated. Data aggregation is a possible way to save energy consumption: nodes may delay data in order to aggregate them into a single packet before forwarding them towards some central node (sink). However, many applications impose constraints on the maximum delay of data; this translates into latency constraints for data arriving at the sink. We study the problem of data aggregation to minimize maximum energy consumption under latency constraints on sensed data delivery, and we assume unique communication paths that form an intree rooted at the sink. We prove that the offline problem is strongly NP-hard and we design a 2-approximation algorithm. The latter uses a novel rounding technique. Almost all real-life sensor networks are managed online by simple distributed algorithms in the nodes. In this context we consider both the case in which sensor nodes are synchronized or not. We assess the performance of the algorithm by competitive analysis. We also provide lower bounds for the models we consider, in some cases showing optimality of the algorithms we propose. Most of our results also hold when minimizing the total energy consumption of all nodes.", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cohen:2009:TDM, author = "Rami Cohen and Dror Rawitz and Danny Raz", title = "Time-dependent multi-scheduling of multicast", journal = j-TALG, volume = "6", number = "1", pages = "14:1--14:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644029", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Many network applications that need to distribute content and data to a large number of clients use a hybrid scheme in which one (or more) multicast channel is used in parallel to a unicast dissemination. This way the application can distribute data using one of its available multicast channels or by sending one or more unicast transmissions. In such a model the utilization of the multicast channels is critical for the overall performance of the system. We study the scheduling algorithm of the sender in such a model. We describe this scheduling problem as an optimization problem where the objective is to maximize the utilization of the multicast channel. Our model captures the fact that it may be beneficial to multicast an object more than once (e.g., page update). Thus, the benefit depends, among other things, on the last time the object was sent, which makes the problem much more complex than previous related scheduling problems. We show that our problem is NP-hard. Then, using the local ratio technique we obtain a 4-approximation algorithm for the case where the objects are of fixed size and a 10-approximation algorithm for the general case. We also consider a special case which may be of practical interest, and prove that a simple greedy algorithm is a 3-approximation algorithm in this case.", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gamzu:2009:IOA, author = "Iftah Gamzu and Danny Segev", title = "Improved online algorithms for the sorting buffer problem on line metrics", journal = j-TALG, volume = "6", number = "1", pages = "15:1--15:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644030", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "An instance of the sorting buffer problem consists of a metric space and a server, equipped with a finite-capacity buffer capable of holding a limited number of requests. An additional ingredient of the input is an online sequence of requests, each of which is characterized by a destination in the given metric space; whenever a request arrives, it must be stored in the sorting buffer. At any point in time, a currently pending request can be served by drawing it out of the buffer and moving the server to its corresponding destination. The objective is to serve all input requests in a way that minimizes the total distance traveled by the server. In this article, we focus our attention on instances of the problem in which the underlying metric is either an evenly-spaced line metric or a continuous line metric. Our main findings can be briefly summarized as follows. (1) We present a deterministic {$ O(\log n) $}-competitive algorithm for {$n$}-point evenly-spaced line metrics. This result improves on a randomized {$ O(\log^2 n) $}-competitive algorithm due to Khandekar and Pandit [2006b]. It also refutes their conjecture, stating that a deterministic strategy is unlikely to obtain a nontrivial competitive ratio. (2) We devise a deterministic {$ O(\log N \log \log N) $}-competitive algorithm for continuous line metrics, where {$N$} denotes the length of the input sequence. In this context, we introduce a novel discretization technique of independent interest. (3) We establish the first nontrivial lower bound for the evenly-spaced case, by proving that the competitive ratio of any deterministic algorithm is at least {$ 2 + \sqrt 3 / \sqrt 3 \approx 2.154 $}. This result settles, to some extent, an open question due to Khandekar and Pandit [2006b], who posed the task of attaining lower bounds on the achievable competitive ratio as a foundational objective for future research.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Andreev:2009:SSL, author = "Konstantin Andreev and Charles Garrod and Daniel Golovin and Bruce Maggs and Adam Meyerson", title = "Simultaneous source location", journal = j-TALG, volume = "6", number = "1", pages = "16:1--16:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644031", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problem of simultaneous source location: selecting locations for sources in a capacitated graph such that a given set of demands can be satisfied simultaneously, with the goal of minimizing the number of locations chosen. For general directed and undirected graphs we give an {$ O(\log D) $}-approximation algorithm, where {$D$} is the sum of demands, and prove matching {$ \Omega (\log D) $} hardness results assuming P {$ \neq $} NP. For undirected trees, we give an exact algorithm and show how this can be combined with a result of R{\"a}cke to give a solution that exceeds edge capacities by at most {$ O(\log^2 n \log \log n) $}, where {$n$} is the number of nodes. For undirected graphs of bounded treewidth we show that the problem is still NP-hard, but we are able to give a PTAS with at most {$ (1 + \epsilon) $} violation of the capacities for arbitrarily small {$ \epsilon $}, or a $ (k + 1) $ approximation with exact capacities, where $k$ is the treewidth.", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bein:2009:KYQ, author = "Wolfgang Bein and Mordecai J. Golin and Lawrence L. Larmore and Yan Zhang", title = "The {Knuth--Yao} quadrangle-inequality speedup is a consequence of total monotonicity", journal = j-TALG, volume = "6", number = "1", pages = "17:1--17:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644032", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "There exist several general techniques in the literature for speeding up naive implementations of dynamic programming. Two of the best known are the Knuth--Yao quadrangle inequality speedup and the SMAWK algorithm for finding the row-minima of totally monotone matrices. Although both of these techniques use a quadrangle inequality and seem similar, they are actually quite different and have been used differently in the literature. In this article we show that the Knuth--Yao technique is actually a direct consequence of total monotonicity. As well as providing new derivations of the Knuth--Yao result, this also permits to solve the Knuth--Yao problem directly using the SMAWK algorithm. Another consequence of this approach is a method for solving online versions of problems with the Knuth--Yao property. The online algorithms given here are asymptotically as fast as the best previously known static ones. For example, the Knuth--Yao technique speeds up the standard dynamic program for finding the optimal binary search tree of $n$ elements from {$ \Theta (n^3) $} down to {$ O(n^2) $}, and the results in this article allow construction of an optimal binary search tree in an online fashion (adding a node to the left or the right of the current nodes at each step) in {$ O(n) $} time per step.", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hassin:2009:AMQ, author = "Refael Hassin and Asaf Levin and Maxim Sviridenko", title = "Approximating the minimum quadratic assignment problems", journal = j-TALG, volume = "6", number = "1", pages = "18:1--18:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644033", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the well-known minimum quadratic assignment problem. In this problem we are given two $ n \times n $ nonnegative symmetric matrices {$ A = (a_{ij}) $} and {$ B = (b_{ij}) $}. The objective is to compute a permutation {$ \pi $} of {$ V = \{ 1, \ldots {}, n \} $} so that {$ \Sigma i, j \in V_{i \neq j} a_{\pi (i), \pi (j)} b_{i, j} $} is minimized. We assume that {$A$} is a {$ 0 / 1 $} incidence matrix of a graph, and that {$B$} satisfies the triangle inequality. We analyze the approximability of this class of problems by providing polynomial bounded approximations for some special cases, and inapproximability results for other cases.", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Alagic:2009:QAS, author = "Gorjan Alagic and Cristopher Moore and Alexander Russell", title = "Quantum algorithms for {Simon}'s problem over nonabelian groups", journal = j-TALG, volume = "6", number = "1", pages = "19:1--19:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644034", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Daniel Simon's 1994 discovery of an efficient quantum algorithm for finding ``hidden shifts'' of Z$_2^n$ provided the first algebraic problem for which quantum computers are exponentially faster than their classical counterparts. In this article, we study the generalization of Simon's problem to arbitrary groups. Fixing a finite group {$G$}, this is the problem of recovering an involution {$ m = (m_1, \ldots {}, m_n) \in G^n $} from an oracle {$f$} with the property that {$ f(x \cdot y) = f(x) \leq y \in \{ 1, m \} $}. In the current parlance, this is the hidden subgroup problem (HSP) over groups of the form {$ G^n $}, where {$G$} is a nonabelian group of constant size, and where the hidden subgroup is either trivial or has order two. Although groups of the form {$ G^n $} have a simple product structure, they share important representation--theoretic properties with the symmetric groups {$ S_n $}, where a solution to the HSP would yield a quantum algorithm for Graph Isomorphism. In particular, solving their HSP with the so-called ``standard method'' requires highly entangled measurements on the tensor product of many coset states. In this article, we provide quantum algorithms with time complexity {2$^{o(\sqrt n)}$} that recover hidden involutions {$ m = (m_1, \ldots {}, m_n) \in G^n $} where, as in Simon's problem, each {$ m_i $} is either the identity or the conjugate of a known element {$m$} which satisfies {$ \kappa (m) = - \kappa (1) $} for some {$ \kappa \in G $}. Our approach combines the general idea behind Kuperberg's sieve for dihedral groups with the ``missing harmonic'' approach of Moore and Russell. These are the first nontrivial HSP algorithms for group families that require highly entangled multiregister Fourier sampling.", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Babai:2009:CRC, author = "L{\'a}szl{\'o} Babai and Pedro F. Felzenszwalb", title = "Computing rank-convolutions with a mask", journal = j-TALG, volume = "6", number = "1", pages = "20:1--20:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644035", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Rank-convolutions have important applications in a variety of areas such as signal processing and computer vision. We define a mask as a function taking only values zero and infinity. Rank-convolutions with masks are of special interest to image processing. We show how to compute the rank-$k$ convolution of a function over an interval of length $n$ with an arbitrary mask of length $m$ in {$ O(n \sqrt m \log m) $} time. The result generalizes to the {$d$}-dimensional case. Previously no algorithm performing significantly better than the brute-force {$ O(n m) $} bound was known. Our algorithm seems to perform well in practice. We describe an implementation, illustrating its application to a problem in image processing. Already on relatively small images, our experiments show a significant speedup compared to brute force.", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bruss:2009:IAI, author = "F. Thomas Bruss and Guy Louchard and Mark Daniel Ward", title = "Inverse auctions: {Injecting} unique minima into random sets", journal = j-TALG, volume = "6", number = "1", pages = "21:1--21:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644036", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider auctions in which the winning bid is the smallest bid that is unique. Only the upper-price limit is given. Neither the number of participants nor the distribution of the offers are known, so that the problem of placing a bid to win with maximum probability looks, a priori, ill-posed. Indeed, the essence of the problem is to inject a (final) minimum into a random subset (of unique offers) of a larger random set. We will see, however, that here no more than two external (and almost compelling) arguments make the problem meaningful. By appropriately modeling the relationship between the number of participants and the distribution of the bids, we can then maximize our chances of winning the auction and propose a computable algorithm for placing our bid.", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Albers:2010:EN, author = "Susanne Albers", title = "Editorial {Note}", journal = j-TALG, volume = "6", number = "2", pages = "22:1--22:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721838", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Mathieu:2010:FSI, author = "Claire Mathieu", title = "Foreword to special issue {SODA} 2009", journal = j-TALG, volume = "6", number = "2", pages = "23:1--23:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721839", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cabello:2010:FSC, author = "Sergio Cabello", title = "Finding shortest contractible and shortest separating cycles in embedded graphs", journal = j-TALG, volume = "6", number = "2", pages = "24:1--24:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721840", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give a polynomial-time algorithm to find a shortest contractible cycle (i.e., a closed walk without repeated vertices) in a graph embedded in a surface. This answers a question posed by Hutchinson. In contrast, we show that finding a shortest contractible cycle through a given vertex is NP-hard. We also show that finding a shortest separating cycle in an embedded graph is NP-hard. This answers a question posed by Mohar and Thomassen.", acknowledgement = ack-nhfb, articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "3-path condition; forbidden pairs; graphs on surfaces; topological graph theory", } @Article{Aspnes:2010:ASM, author = "James Aspnes and Keren Censor", title = "Approximate shared-memory counting despite a strong adversary", journal = j-TALG, volume = "6", number = "2", pages = "25:1--25:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721841", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A new randomized asynchronous shared-memory data structure is given for implementing an approximate counter that can be incremented once by each of $n$ processes in a model that allows up to $ n - 1 $ crash failures. For any fixed $ \epsilon $, the counter achieves a relative error of $ \delta $ with high probability, at the cost of {$ O(((1 / \delta) \log n)^{O(1 / \epsilon)}) $} register operations per increment and {$ O(n^{4 / 5 + \epsilon }((1 / \delta) \log n)^{O(1 / \epsilon)}) $} register operations per read. The counter combines randomized sampling for estimating large values with an expander for estimating small values. This is the first counter implementation that is sublinear the number of processes and works despite a strong adversary scheduler that can observe internal states of processes.\par An application of the improved counter is an improved protocol for solving randomized shared-memory consensus, which reduces the best previously known individual work complexity from {$ O(n \log n) $} to an optimal {$ O(n) $}, resolving one of the last remaining open problems concerning consensus in this model.", acknowledgement = ack-nhfb, articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximate counting; consensus; Distributed computing; expanders; martingales", } @Article{Chan:2010:CBT, author = "Timothy M. Chan", title = "Comparison-based time-space lower bounds for selection", journal = j-TALG, volume = "6", number = "2", pages = "26:1--26:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721842", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We establish the first nontrivial lower bounds on time-space trade-offs for the selection problem. We prove that any comparison-based randomized algorithm for finding the median requires {$ \Omega (n \log \log_S n) $} expected time in the RAM model (or more generally in the comparison branching program model), if we have {$S$} bits of extra space besides the read-only input array. This bound is tight for all {$ S > \log n $}, and remains true even if the array is given in a random order. Our result thus answers a 16-year-old question of Munro and Raman [1996], and also complements recent lower bounds that are restricted to sequential access, as in the multipass streaming model [Chakrabarti et al. 2008b].\par We also prove that any comparison-based, deterministic, multipass streaming algorithm for finding the median requires {$ \Omega (n \log^*(n / s) + n \log_s n) $} worst-case time (in scanning plus comparisons), if we have {$s$} cells of space. This bound is also tight for all {$ s > \log^2 n $}. We get deterministic lower bounds for I/O-efficient algorithms as well.\par The proofs in this article are self-contained and do not rely on communication complexity techniques.", acknowledgement = ack-nhfb, articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Adversary arguments; lower bounds; median finding; RAM; randomized algorithms; streaming algorithms; time--space trade-offs", } @Article{Goel:2010:PMU, author = "Ashish Goel and Michael Kapralov and Sanjeev Khanna", title = "Perfect matchings via uniform sampling in regular bipartite graphs", journal = j-TALG, volume = "6", number = "2", pages = "27:1--27:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721843", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article we further investigate the well-studied problem of finding a perfect matching in a regular bipartite graph. The first nontrivial algorithm, with running time {$ O(m n) $}, dates back to K{\"o}nig's work in 1916 (here {$ m = n d $} is the number of edges in the graph, {$ 2^n $} is the number of vertices, and {$d$} is the degree of each node). The currently most efficient algorithm takes time {$ O(m) $}, and is due to Cole et al. [2001]. We improve this running time to {$ O(\min \{ m, n^{2.5} \ln n / d \}) $}; this minimum can never be larger than {$ O(n^{1.75} \sqrt {\ln n}) $}. We obtain this improvement by proving a uniform sampling theorem: if we sample each edge in a {$d$}-regular bipartite graph independently with a probability {$ p = O(n \ln n / d^2) $} then the resulting graph has a perfect matching with high probability. The proof involves a decomposition of the graph into pieces which are guaranteed to have many perfect matchings but do not have any small cuts. We then establish a correspondence between potential witnesses to nonexistence of a matching (after sampling) in any piece and cuts of comparable size in that same piece. Karger's sampling theorem [1994a, 1994b] for preserving cuts in a graph can now be adapted to prove our uniform sampling theorem for preserving perfect matchings. Using the {$ O(m \sqrt n) $} algorithm (due to Hopcroft and Karp [1973]) for finding maximum matchings in bipartite graphs on the sampled graph then yields the stated running time. We also provide an infinite family of instances to show that our uniform sampling result is tight up to polylogarithmic factors (in fact, up to {$ l n^2 n $} ).", acknowledgement = ack-nhfb, articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Perfect matching; regular bipartite graphs", } @Article{Aminof:2010:RAO, author = "Benjamin Aminof and Orna Kupferman and Robby Lampert", title = "Reasoning about online algorithms with weighted automata", journal = j-TALG, volume = "6", number = "2", pages = "28:1--28:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721844", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We describe an automata-theoretic approach for the competitive analysis of {\em online algorithms}. Our approach is based on {\em weighted automata}, which assign to each input word a cost in {$ R^{\geq 0} $}. By relating the ``unbounded look ahead'' of optimal offline algorithms with nondeterminism, and relating the ``no look ahead'' of online algorithms with determinism, we are able to solve problems about the competitive ratio of online algorithms, and the memory they require, by reducing them to questions about {\em determinization\/} and {\em approximated determinization\/} of weighted automata.", acknowledgement = ack-nhfb, articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Formal verification; online algorithms; weighted automata", } @Article{Marx:2010:AFH, author = "D{\'a}niel Marx", title = "Approximating fractional hypertree width", journal = j-TALG, volume = "6", number = "2", pages = "29:1--29:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721845", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Fractional hypertree width is a hypergraph measure similar to tree width and hypertree width. Its algorithmic importance comes from the fact that, as shown in previous work, Constraint Satisfaction Problems (CSP) and various problems in database theory are polynomial-time solvable if the input contains a bounded-width fractional hypertree decomposition of the hypergraph of the constraints. In this article, we show that for every fixed $ w \geq 1 $, there is a polynomial-time algorithm that, given a hypergraph {$H$} with fractional hypertree width at most {$w$}, computes a fractional hypertree decomposition of width {$ O(w^3) $} for {$H$}. This means that polynomial-time algorithms relying on bounded-width fractional hypertree decompositions no longer need to be given a decomposition explicitly in the input, since an appropriate decomposition can be computed in polynomial time. Therefore, if {$H$} is a class of hypergraphs with bounded fractional hypertree width, then a CSP restricted to instances whose structure is in {$H$} is polynomial-time solvable. This makes bounded fractional hypertree width the most general known hypergraph property that makes CSP, Boolean conjunctive queries, and conjunctive query containment polynomial-time solvable.", acknowledgement = ack-nhfb, articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "constraint satisfaction; fractional hypertree width; Treewidth", } @Article{Klein:2010:SPD, author = "Philip N. Klein and Shay Mozes and Oren Weimann", title = "Shortest paths in directed planar graphs with negative lengths: a linear-space {$ O(n \log^2 n) $}-time algorithm", journal = j-TALG, volume = "6", number = "2", pages = "30:1--30:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721846", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give an {$ O(n \log^2 n) $}-time, linear-space algorithm that, given a directed planar graph with positive and negative arc-lengths, and given a node {$s$}, finds the distances from {$s$} to all nodes.", acknowledgement = ack-nhfb, articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Monge; Planar graphs; replacement paths; shortest paths", } @Article{Panagiotou:2010:MBS, author = "Konstantinos Panagiotou and Angelika Steger", title = "Maximal biconnected subgraphs of random planar graphs", journal = j-TALG, volume = "6", number = "2", pages = "31:1--31:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721847", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Let {$C$} be a class of labeled connected graphs, and let {$ C_n $} be a graph drawn uniformly at random from graphs in {$C$} that contain exactly {$n$} vertices. Denote by {$ b(\ell; C_n) $} the number of blocks (i.e., maximal biconnected subgraphs) of {$ C_n $} that contain exactly {$ \ell $} vertices, and let {$ l b(C_n) $} be the number of vertices in a largest block of {$ C_n $}. We show that under certain general assumptions on {$C$}, {$ C_n $} belongs with high probability to one of the following categories:\par (1) {$ l b(C_n) \sim c n $}, for some explicitly given {$ c = c(C) $}, and the second largest block is of order {$ n^\alpha $}, where {$ 1 > \alpha = \alpha (C) $}, or\par (2) {$ l b(C_n) = O(\log n) $}, that is, all blocks contain at most logarithmically many vertices.\par Moreover, in both cases we show that the quantity {$ b(\ell; C_n) $} is concentrated for all {$ \ell $} and we determine its expected value. As a corollary we obtain that the class of planar graphs belongs to category {$1$}. In contrast to that, outerplanar and series-parallel graphs belong to category {$1$}.", acknowledgement = ack-nhfb, articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Graphs with constraints; planar graphs; random structures", } @Article{Thomasse:2010:KFV, author = "St{\'e}phan Thomass{\'e}", title = "A $ 4 k^2 $ kernel for feedback vertex set", journal = j-TALG, volume = "6", number = "2", pages = "32:1--32:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721848", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:49:22 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We prove that given an undirected graph {$G$} on {$n$} vertices and an integer {$k$}, one can compute, in polynomial time in {$n$}, a graph {$ G \prime $} with at most {$ 4 k^2 $} vertices and an integer {$ k \prime $} such that {$G$} has a feedback vertex set of size at most {$ k \iff G \prime $} has a feedback vertex set of size at most {$ k \prime $}. This result improves a previous {$ O(k^{11}) $} kernel of Burrage et al., and a more recent cubic kernel of Bodlaender. This problem was communicated by Fellows.", acknowledgement = ack-nhfb, articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "feedback vertex set; fixed parameter tractability; Kernelization; matching", } @Article{Thomasse:2010:KKF, author = "St{\'e}phan Thomass{\'e}", title = "A $ 4 k^2 $ kernel for feedback vertex set", journal = j-TALG, volume = "6", number = "2", pages = "32:1--32:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721848", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We prove that given an undirected graph {$G$} on {$n$} vertices and an integer {$k$}, one can compute, in polynomial time in {$n$}, a graph {$ G' $} with at most {$ 4 k^2 $} vertices and an integer {$ k' $} such that {$G$} has a feedback vertex set of size at most {$k$} iff {$ G' $} has a feedback vertex set of size at most {$ k' $}. This result improves a previous {$ O(k^{11}) $} kernel of Burrage et al., and a more recent cubic kernel of Bodlaender. This problem was communicated by Fellows.", acknowledgement = ack-nhfb, articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Madani:2010:DDM, author = "Omid Madani and Mikkel Thorup and Uri Zwick", title = "Discounted deterministic {Markov} decision processes and discounted all-pairs shortest paths", journal = j-TALG, volume = "6", number = "2", pages = "33:1--33:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721849", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present algorithms for finding optimal strategies for discounted, infinite-horizon, Determinsitc Markov Decision Processes (DMDPs). Our fastest algorithm has a worst-case running time of {$ O(m n) $}, improving the recent bound of {$ O(m n^2) $} obtained by Andersson and Vorbyov [2006]. We also present a randomized {$ O(m^{1 / 2} n^2) $}-time algorithm for finding Discounted All-Pairs Shortest Paths (DAPSP), improving an {$ O(m n^2) $}-time algorithm that can be obtained using ideas of Papadimitriou and Tsitsiklis [1987].", acknowledgement = ack-nhfb, articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Markov decision processes; minimum mean weight cycles; shortest paths", } @Article{Shalita:2010:EAG, author = "Alon Shalita and Uri Zwick", title = "Efficient algorithms for the 2-gathering problem", journal = j-TALG, volume = "6", number = "2", pages = "34:1--34:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721850", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Pebbles are placed on some vertices of a directed graph. Is it possible to move each pebble along at most one edge of the graph so that in the final configuration no pebble is left on its own? We give an {$ O(m n) $}-time algorithm for solving this problem, which we call the {\em 2-gathering\/} problem, where {$n$} is the number of vertices and {$m$} is the number of edges of the graph. If such a 2-gathering is not possible, the algorithm finds a solution that minimizes the number of solitary pebbles. The 2-gathering problem forms a nontrivial generalization of the nonbipartite matching problem and it is solved by extending the augmenting paths technique used to solve matching problems.", acknowledgement = ack-nhfb, articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "2-gatherings; augmenting paths; nonbipartite matchings", } @Article{Bansal:2010:DPI, author = "Nikhil Bansal and Ning Chen and Neva Cherniavsky and Atri Rurda and Baruch Schieber and Maxim Sviridenko", title = "Dynamic pricing for impatient bidders", journal = j-TALG, volume = "6", number = "2", pages = "35:1--35:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721851", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the following problem related to pricing over time. Assume there is a collection of bidders, each of whom is interested in buying a copy of an item of which there is an unlimited supply. Every bidder is associated with a time interval over which the bidder will consider buying a copy of the item, and a maximum value the bidder is willing to pay for the item. On every time unit, the seller sets a price for the item. The seller's goal is to set the prices so as to maximize revenue from the sale of copies of items over the time period.\par In the first model considered, we assume that all bidders are {\em impatient}, that is, bidders buy the item at the first time unit within their bid interval that they can afford the price. To the best of our knowledge, this is the first work that considers this model. In the offline setting, we assume that the seller knows the bids of all the bidders in advance. In the online setting we assume that at each time unit the seller only knows the values of the bids that have arrived before or at that time unit. We give a polynomial time offline algorithm and prove upper and lower bounds on the competitiveness of deterministic and randomized online algorithms, compared with the optimal offline solution. The gap between the upper and lower bounds is quadratic.\par We also consider the {\em envy-free\/} model in which bidders are sold the item at the minimum price during their bid interval, as long as it is not over their limit value. We prove tight bounds on the competitiveness of deterministic online algorithms for this model, and upper and lower bounds on the competitiveness of randomized algorithms with quadratic gap. The lower bounds for the randomized case in both models use a novel general technique.", acknowledgement = ack-nhfb, articleno = "35", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Digital goods; online algorithms; pricing", } @Article{Azar:2010:TUF, author = "Yossi Azar and Iftah Gamzu and Shai Gutner", title = "Truthful unsplittable flow for large capacity networks", journal = j-TALG, volume = "6", number = "2", pages = "36:1--36:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721852", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The {\em unsplittable flow problem\/} is one of the most extensively studied optimization problems in the field of networking. An instance of it consists of an edge capacitated graph and a set of connection requests, each of which is associated with source and target vertices, a demand, and a value. The objective is to route a maximum value subset of requests subject to the edge capacities. It is a well known fact that as the capacities of the edges are larger with respect to the maximal demand among the requests, the problem can be approximated better. In particular, it is known that for sufficiently large capacities, the integrality gap of the corresponding integer linear program becomes $ 1 + \epsilon $, which can be matched by an algorithm that utilizes the randomized rounding technique.\par In this article, we focus our attention on the large capacities unsplittable flow problem in a game theoretic setting. In this setting, there are selfish agents, which control some of the requests characteristics, and may be dishonest about them. It is worth noting that in game theoretic settings many standard techniques, such as randomized rounding, violate certain monotonicity properties, which are imperative for truthfulness, and therefore cannot be employed. In light of this state of affairs, we design a monotone deterministic algorithm, which is based on a primal-dual machinery, which attains an approximation ratio of $ e / (e - 1) $, up to a disparity of $ \epsilon $ away. This implies an improvement on the current best truthful mechanism, as well as an improvement on the current best combinatorial algorithm for the problem under consideration. Surprisingly, we demonstrate that any algorithm in the family of reasonable iterative path minimizing algorithms, cannot yield a better approximation ratio. Consequently, it follows that in order to achieve a monotone PTAS, if that exists, one would have to exert different techniques. We also consider the large capacities {\em single-minded multi-unit combinatorial auction problem}. This problem is closely related to the unsplittable flow problem since one can formulate it as a special case of the integer linear program of the unsplittable flow problem. Accordingly, we obtain a comparable performance guarantee by refining the algorithm suggested for the unsplittable flow problem.", acknowledgement = ack-nhfb, articleno = "36", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithms; combinatorial and multi-unit auctions; Mechanism design; primal-dual method", } @Article{Svitkina:2010:FLH, author = "Zoya Svitkina and {\'E}va Tardos", title = "Facility location with hierarchical facility costs", journal = j-TALG, volume = "6", number = "2", pages = "37:1--37:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721853", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce a facility location problem with submodular facility cost functions, and give an {$ O(\log n) $} approximation algorithm for it. Then we focus on a special case of submodular costs, called hierarchical facility costs, and give a {$ (4.237 + \epsilon) $}-approximation algorithm using local search. The hierarchical facility costs model multilevel service installation. Shmoys et al. [2004] gave a constant factor approximation algorithm for a two-level version of the problem. Here we consider a multilevel problem, and give a constant factor approximation algorithm, independent of the number of levels, for the case of identical costs on all facilities.", acknowledgement = ack-nhfb, articleno = "37", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithm; facility location; local search; submodular function", } @Article{Christodoulou:2010:MDF, author = "George Christodoulou and Elias Koutsoupias and Annam{\'a}ria Kov{\'a}cs", title = "Mechanism design for fractional scheduling on unrelated machines", journal = j-TALG, volume = "6", number = "2", pages = "38:1--38:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721854", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Scheduling on unrelated machines is one of the most general and classical variants of the task scheduling problem. Fractional scheduling is the LP-relaxation of the problem, which is polynomially solvable in the nonstrategic setting, and is a useful tool to design deterministic and randomized approximation algorithms.\par The mechanism design version of the scheduling problem was introduced by Nisan and Ronen. In this article, we consider the mechanism design version of the fractional variant of this problem. We give lower bounds for any fractional truthful mechanism. Our lower bounds also hold for any (randomized) mechanism for the integral case. In the positive direction, we propose a truthful mechanism that achieves approximation 3/2 for 2 machines, matching the lower bound. This is the first new tight bound on the approximation ratio of this problem, after the tight bound of 2, for 2 machines, obtained by Nisan and Ronen. For $n$ machines, our mechanism achieves an approximation ratio of $ n + 1 / 2 $.\par Motivated by the fact that all the known deterministic and randomized mechanisms for the problem assign each task independently from the others, we focus on an interesting subclass of allocation algorithms, the {\em task-independent\/} algorithms. We give a lower bound of $ n + 1 / 2 $, that holds for every (not only monotone) allocation algorithm that takes independent decisions. Under this consideration, our truthful independent mechanism is the best that we can hope from this family of algorithms.", acknowledgement = ack-nhfb, articleno = "38", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "scheduling; Truthful mechanisms; unrelated machines", } @Article{Korman:2010:LSV, author = "Amos Korman", title = "Labeling schemes for vertex connectivity", journal = j-TALG, volume = "6", number = "2", pages = "39:1--39:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721855", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article studies labeling schemes for the vertex connectivity function on general graphs. We consider the problem of assigning short labels to the nodes of any $n$-node graph is such a way that given the labels of any two nodes $u$ and $v$, one can decide whether $u$ and $v$ are $k$-vertex connected in {$G$}, that is, whether there exist {$k$} vertex disjoint paths connecting {$u$} and {$v$}. This article establishes an upper bound of $ k^2 \log n $ on the number of bits used in a label. The best previous upper bound for the label size of such a labeling scheme is $ 2^k \log n $.", acknowledgement = ack-nhfb, articleno = "39", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Graph algorithms; labeling schemes; vertex-connectivity", } @Article{Butman:2010:OPM, author = "Ayelet Butman and Danny Hermelin and Moshe Lewenstein and Dror Rawitz", title = "Optimization problems in multiple-interval graphs", journal = j-TALG, volume = "6", number = "2", pages = "40:1--40:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721856", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Multiple-interval graphs are a natural generalization of interval graphs where each vertex may have more then one interval associated with it. We initiate the study of optimization problems in multiple-interval graphs by considering three classical problems: Minimum Vertex Cover, Minimum Dominating Set, and Maximum Clique. We describe applications for each one of these problems, and then proceed to discuss approximation algorithms for them.\par Our results can be summarized as follows: Let $t$ be the number of intervals associated with each vertex in a given multiple-interval graph. For Minimum Vertex Cover, we give a $ (2 - 1 / t) $-approximation algorithm which also works when a $t$-interval representation of our given graph is absent. Following this, we give a $ t^2 $-approximation algorithm for Minimum Dominating Set which adapts well to more general variants of the problem. We then proceed to prove that Maximum Clique is NP-hard already for 3-interval graphs, and provide a $ t^2 - (t + 1) / 2 $-approximation algorithm for general values of $ t \geq 2 $, using bounds proven for the so-called transversal number of $t$-interval families.", acknowledgement = ack-nhfb, articleno = "40", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "$t$-interval graphs; Approximation algorithms; maximum clique; minimum dominating set; minimum vertex cover; multiple-interval graphs", } @Article{Gupta:2010:DRF, author = "Anupam Gupta and Mohammadtaghi Hajiaghayi and Viswanath Nagarajan and R. Ravi", title = "Dial a {Ride} from $k$-forest", journal = j-TALG, volume = "6", number = "2", pages = "41:1--41:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721857", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:49:22 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The {\em $k$-forest problem\/} is a common generalization of both the $k$-MST and the {\em dense-$k$-subgraph\/} problems. Formally, given a metric space on $n$ vertices {$V$}, with {$m$} demand pairs {$ \subseteq V \times V $} and a ``target'' {$ k \leq m $}, the goal is to find a minimum cost subgraph that connects {\em at least\/} {$k$} pairs. In this paper, we give an {$ O(m i n \{ \sqrt n \cdot \log k, \sqrt k \}) $}-approximation algorithm for {$k$}-forest, improving on the previous best ratio of {$ O(m i n \{ n^{2 / 3}, \sqrt m \log n \}) $} by Segev and Segev.\par We then apply our algorithm for {$k$}-forest to obtain approximation algorithms for several {\em Dial-a-Ride\/} problems. The basic Dial-a-Ride problem is the following: given an {$n$} point metric space with {$m$} objects each with its own source and destination, and a vehicle capable of carrying {\em at most\/} $k$ objects at any time, find the minimum length tour that uses this vehicle to move each object from its source to destination. We want that the tour be {\em non-preemptive\/}: that is, each object, once picked up at its source, is dropped only at its destination. We prove that an $ \alpha $-approximation algorithm for the $k$-forest problem implies an {$ O(\alpha \cdot \log^2 n) $}-approximation algorithm for Dial-a-Ride. Using our results for {$k$}-forest, we get an {$ O(m i n \{ \sqrt n, \sqrt k \} \cdot \log^2 n) $}-approximation algorithm for Dial-a-Ride. The only previous result known for Dial-a-Ride was an {$ O(\sqrt k \log n) $}-approximation by Charikar and Raghavachari; our results give a different proof of a similar approximation guarantee --- in fact, when the vehicle capacity {$k$} is large, we give a slight improvement on their results. The reduction from Dial-a-Ride to the {$k$}-forest problem is fairly robust, and allows us to obtain approximation algorithms (with the same guarantee) for some interesting generalizations of Dial-a-Ride.", acknowledgement = ack-nhfb, articleno = "41", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; network design; vehicle routing", } @Article{Gupta:2010:DRK, author = "Anupam Gupta and Mohammadtaghi Hajiaghayi and Viswanath Nagarajan and R. Ravi", title = "Dial a {Ride} from $k$-forest", journal = j-TALG, volume = "6", number = "2", pages = "41:1--41:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721857", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The $k$-forest problem is a common generalization of both the $k$-MST and the dense-$k$-subgraph problems. Formally, given a metric space on $n$ vertices {$V$}, with {$m$} demand pairs {$ \subseteq V \times V $} and a ``target'' {$ k \leq m $}, the goal is to find a minimum cost subgraph that connects at least {$k$} pairs. In this paper, we give an {$ O(m i n{\sqrt n \cdot \log k, \sqrt k}) $}-approximation algorithm for {$k$}-forest, improving on the previous best ratio of {$ O(m i n \{ n^{2 / 3}, \sqrt m \} \log n) $} by Segev and Segev. We then apply our algorithm for {$k$}-forest to obtain approximation algorithms for several Dial-a-Ride problems. The basic Dial-a-Ride problem is the following: given an {$n$} point metric space with {$m$} objects each with its own source and destination, and a vehicle capable of carrying at most $k$ objects at any time, find the minimum length tour that uses this vehicle to move each object from its source to destination. We want that the tour be non-preemptive: that is, each object, once picked up at its source, is dropped only at its destination. We prove that an $ \alpha $-approximation algorithm for the $k$-forest problem implies an {$ O(\alpha \cdot \log^2 n) $}-approximation algorithm for Dial-a-Ride. Using our results for {$k$}-forest, we get an {$ O(\min \{ \sqrt n, \sqrt k \} \cdot \log^2 n) $}-approximation algorithm for Dial-a-Ride. The only previous result known for Dial-a-Ride was an {$ O(\sqrt k \log n) $}-approximation by Charikar and Raghavachari; our results give a different proof of a similar approximation guarantee-in fact, when the vehicle capacity {$k$} is large, we give a slight improvement on their results. The reduction from Dial-a-Ride to the {$k$}-forest problem is fairly robust, and allows us to obtain approximation algorithms (with the same guarantee) for some interesting generalizations of Dial-a-Ride.", acknowledgement = ack-nhfb, articleno = "41", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bobier:2010:FAG, author = "Bruce Bobier and Joe Sawada", title = "A fast algorithm to generate open meandric systems and meanders", journal = j-TALG, volume = "6", number = "2", pages = "42:1--42:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721858", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "An open meandric system is a planar configuration of acyclic curves crossing an infinite horizontal line in the plane such that the curves may extend in both horizontal directions. We present a fast, recursive algorithm to exhaustively generate open meandric systems with $n$ crossings. We then illustrate how to modify the algorithm to generate unidirectional open meandric systems (the curves extend only to the right) and nonisomorphic open meandric systems where equivalence is taken under horizontal reflection. Each algorithm can be modified to generate systems with exactly $k$ curves. In the unidirectional case when $ k = 1 $, we can apply a minor modification along with some additional optimization steps to yield the first fast and simple algorithm to generate open meanders.", acknowledgement = ack-nhfb, articleno = "42", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "CAT algorithm; meander; open meandric system", } @Article{Ergun:2010:PTS, author = "Funda Ergun and S. Muthukrishnan and Cenk Sahinalp", title = "Periodicity testing with sublinear samples and space", journal = j-TALG, volume = "6", number = "2", pages = "43:1--43:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721859", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this work, we are interested in periodic trends in long data streams in the presence of computational constraints. To this end; we present algorithms for discovering periodic trends in the combinatorial property testing model in a data stream {$S$} of length {$n$} using {$ o(n) $} samples and space.\par In accordance with the property testing model, we first explore the notion of being ``close'' to periodic by defining three different notions of self-distance through relaxing different notions of exact periodicity. An input {$S$} is then called approximately periodic if it exhibits a small self-distance (with respect to any one self-distance defined). We show that even though the different definitions of exact periodicity are equivalent, the resulting definitions of self-distance and approximate periodicity are not; we also show that these self-distances are constant approximations of each other. Afterwards, we present algorithms which distinguish between the two cases where {$S$} is exactly periodic and {$S$} is far from periodic with only a constant probability of error.\par Our algorithms sample only {$ O(\sqrt n \log^2 n) $} (or {$ O(\sqrt n \log^4 n) $}, depending on the self-distance) positions and use as much space. They can also find, using {$ o(n) $} samples and space, the largest/smallest period, and/or all of the approximate periods of {$S$}. These algorithms can also be viewed as working on streaming inputs where each data item is seen once and in order, storing only a sublinear ({$ O(\sqrt n \log^2 n) $} or {$ O(\sqrt n \log^4 n) $}) size sample from which periodicities are identified.", acknowledgement = ack-nhfb, articleno = "43", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Combinatorial property testing; periodicity", } @Article{Vassilevska:2010:FHS, author = "Virginia Vassilevska and Ryan Williams and Raphael Yuster", title = "Finding heaviest {$H$}-subgraphs in real weighted graphs, with applications", journal = j-TALG, volume = "6", number = "3", pages = "44:1--44:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798597", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "For a graph {$G$} with real weights assigned to the vertices (edges), the MAX {$H$}-SUBGRAPH problem is to find an {$H$}-subgraph of {$G$} with maximum total weight, if one exists. Our main results are new strongly polynomial algorithms for the MAX {$H$}-SUBGRAPH problem. Some of our algorithms are based, in part, on fast matrix multiplication.\par For vertex-weighted graphs with {$n$} vertices we solve a more general problem: the {\em all pairs\/} MAX {$H$}-SUBGRAPH problem, where the task is to find for every pair of vertices {$ u, v $}, a maximum {$H$}-subgraph containing both {$u$} and {$v$}, if one exists. We obtain an {$ O(n^t(\omega, h)) $}-time algorithm for the {\em all pairs\/} MAX {$H$}-SUBGRAPH problem in the case where {$H$} is a fixed graph with {$h$} vertices and {$ \omega $}.\par We also present improved algorithms for the MAX {$H$}-SUBGRAPH problem in the edge-weighted case. In particular, we obtain an {$ O(m^{2 - 1 / k \log n}) $}-time algorithm for the heaviest cycle of length 2 {$k$} or {$ 2 k - 1 $} in a graph with {$m$} edges and an {$ O(n^3 / \log n) $}-time randomized algorithm for finding the heaviest cycle of any fixed length.\par Our methods also yield efficient algorithms for several related problems that are faster than any previously existing algorithms. For example, we show how to find chromatic {$H$}-subgraphs in edge-colored graphs, and how to compute the most significant bits of the distance product of two real matrices, in truly subcubic time.", acknowledgement = ack-nhfb, articleno = "44", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "H-subgraph; matrix multiplication; weighted graph", } @Article{Ruskey:2010:EUC, author = "Frank Ruskey and Aaron Williams", title = "An explicit universal cycle for the $ (n - 1) $-permutations of an $n$-set", journal = j-TALG, volume = "6", number = "3", pages = "45:1--45:12", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798598", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show how to construct an {\em explicit\/} Hamilton cycle in the directed Cayley graph {$ \vec {\rm Cay}(\sigma_n, \sigma_{n - 1} : S_n) $}, where {$ \sigma_k $} is the rotation {$ (1 2 \cdots k) $}. The existence of such cycles was shown by Jackson [1996] but the proof only shows that a certain directed graph is Eulerian, and Knuth [2005] asks for an explicit construction. We show that a simple recursion describes our Hamilton cycle and that the cycle can be generated by an iterative algorithm that uses {$ O(n) $} space. Moreover, the algorithm produces each successive edge of the cycle in constant time; such algorithms are said to be {\em loopless}. Finally, our Hamilton cycle can be used to construct an explicit universal cycle for the {$ (n - 1) $}-permutations of a {$n$}-set, or as the basis of an efficient algorithm for generating every {$n$}-permutation of an $n$-set within a circular array or linked list.", acknowledgement = ack-nhfb, articleno = "45", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "loopless algorithm; Universal cycle", } @Article{Drescher:2010:AAM, author = "Matthew Drescher and Adrian Vetta", title = "An approximation algorithm for the maximum leaf spanning arborescence problem", journal = j-TALG, volume = "6", number = "3", pages = "46:1--46:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798599", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present an {$ O(\sqrt {{\rm opt}}) $}-approximation algorithm for the maximum leaf spanning arborescence problem, where opt is the number of leaves in an optimal spanning arborescence. The result is based upon an {$ O(1) $}-approximation algorithm for a special class of directed graphs called willows. Incorporating the method for willow graphs as a subroutine in a local improvement algorithm gives the bound for general directed graphs.", acknowledgement = ack-nhfb, articleno = "46", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation Algorithms; arborescence; directed graphs; maximum leaf", } @Article{Naor:2010:DCA, author = "Joseph (Seffi) Naor and Roy Schwartz", title = "The directed circular arrangement problem", journal = j-TALG, volume = "6", number = "3", pages = "47:1--47:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798600", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problem of embedding a directed graph onto evenly spaced points on a circle while minimizing the total weighted edge length. We present the first poly-logarithmic approximation factor algorithm for this problem which yields an approximation factor of {$ O(\log n \log \log n) $}, thus improving the previous {$ \tilde {O}(\sqrt n) $} approximation factor. In order to achieve this, we introduce a new problem which we call the {\em directed penalized linear arrangement}. This problem generalizes both the directed feedback edge set problem and the directed linear arrangement problem. We present an {$ O(\log n \log \log n) $}-approximation factor algorithm for this newly defined problem. Our solution uses two distinct directed metrics (``right'' and ``left'') which together yield a lower bound on the value of an optimal solution. In addition, we define a sequence of new directed spreading metrics that are used for applying the algorithm recursively on smaller subgraphs. The new spreading metrics allow us to define an asymmetric region growing procedure that accounts simultaneously for both incoming and outgoing edges. To the best of our knowledge, this is the first time that a region growing procedure is defined in directed graphs that allows for such an accounting.", acknowledgement = ack-nhfb, articleno = "47", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "region growing; scheduling; Spreading metrics", } @Article{Azar:2010:DEC, author = "Yossi Azar and Shay Kutten and Boaz Patt-Shamir", title = "Distributed error confinement", journal = j-TALG, volume = "6", number = "3", pages = "48:1--48:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798601", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study error confinement in distributed applications, which can be viewed as an extreme case of various fault locality notions studied in the past. Error confinement means that to the external observer, only nodes that were directly hit by a fault may deviate from their specified correct behavior, and only temporarily. The externally observable behavior of all other nodes must remain impeccable, even though their internal state may be affected. Error confinement is impossible if an adversary is allowed to inflict arbitrary transient faults on the system, since the faults might completely wipe out input values. We introduce a new fault-tolerance measure we call {\em agility}, which quantifies the fault tolerance of an algorithm that disseminates information against state corrupting faults.\par We then propose broadcast algorithms that guarantee error confinement with optimal agility to within a constant factor in synchronous networks. These algorithms can serve as building blocks in more general reactive systems. Previous results in exploring locality in reactive systems were not error confined, or allowed a wide range of behaviors to be considered correct. Our results also include a new technique that can be used to analyze the ``cow path'' problem.", acknowledgement = ack-nhfb, articleno = "48", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Distributed algorithms; persistence; self-stabilization; voting", } @Article{Aggarwal:2010:AAC, author = "Gagan Aggarwal and Rina Panigrahy and Tom{\'a}s Feder and Dilys Thomas and Krishnaram Kenthapadi and Samir Khuller and An Zhu", title = "Achieving anonymity via clustering", journal = j-TALG, volume = "6", number = "3", pages = "49:1--49:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798602", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Publishing data for analysis from a table containing personal records, while maintaining individual privacy, is a problem of increasing importance today. The traditional approach of deidentifying records is to remove identifying fields such as social security number, name, etc. However, recent research has shown that a large fraction of the U.S. population can be identified using nonkey attributes (called quasi-identifiers) such as date of birth, gender, and zip code. The $k$-anonymity model protects privacy via requiring that nonkey attributes that leak information are suppressed or generalized so that, for every record in the modified table, there are at least $k$-1 other records having exactly the same values for quasi-identifiers. We propose a new method for anonymizing data records, where quasi-identifiers of data records are first clustered and then cluster centers are published. To ensure privacy of the data records, we impose the constraint that each cluster must contain no fewer than a prespecified number of data records. This technique is more general since we have a much larger choice for cluster centers than $k$-anonymity. In many cases, it lets us release a lot more information without compromising privacy. We also provide constant factor approximation algorithms to come up with such a clustering. This is the first set of algorithms for the anonymization problem where the performance is independent of the anonymity parameter $k$. We further observe that a few outlier points can significantly increase the cost of anonymization. Hence, we extend our algorithms to allow an $ \epsilon $ fraction of points to remain unclustered, that is, deleted from the anonymized publication. Thus, by not releasing a small fraction of the database records, we can ensure that the data published for analysis has less distortion and hence is more useful. Our approximation algorithms for new clustering objectives are of independent interest and could be applicable in other clustering scenarios as well.", acknowledgement = ack-nhfb, articleno = "49", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "anonymity; approximation algorithms; clustering; Privacy", } @Article{Gordon:2010:CWT, author = "Eyal Gordon and Adi Ros{\'e}n", title = "Competitive weighted throughput analysis of greedy protocols on {DAGs}", journal = j-TALG, volume = "6", number = "3", pages = "50:1--50:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798603", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The combination of the buffer sizes of routers deployed in the Internet, and the Internet traffic itself, leads routinely to the dropping of packets. Motivated by this, we are interested in the problem of maximizing the throughput of protocols that control packet networks. Moreover, we are interested in a setting where different packets have different priorities (or weights), thus taking into account Quality-of-Service considerations.\par We first extend the Competitive Network Throughput (CNT) model introduced by Aiello et al. [2003] to the weighted packets case. We analyze the performance of online, local-control protocols by their competitive ratio, in the face of arbitrary traffic, using as a measure the total weight of the packets that arrive to their destinations, rather than being dropped en-route. We prove that on Directed Acyclic Graphs (DAGs), any greedy protocol is competitive, with competitive ratio independent of the weights of the packets. Here we mean by a ``greedy protocol'' a protocol that not only does not leave a resource idle unnecessarily, but also prefers packets with higher weight over those with lower weight. We give two independent upper bounds on the competitive ratio of general greedy protocols on DAGs. We further give lower bounds that show that our upper bounds cannot be improved (other than constant factors) in the general case. Both our upper and lower bounds apply also to the unweighted case, and they improve the results given in Aiello et al. [2003] for that case. We thus give tight (up to constant factors) upper and lower bounds for both the unweighted and weighted cases.\par In the course of proving our upper bounds we prove a lemma that gives upper bounds on the delivery times of packets by any greedy protocol on general DAGs (without buffer size considerations). We believe that this lemma may be of independent interest and may find additional applications.", acknowledgement = ack-nhfb, articleno = "50", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Buffer management; competitive analysis; competitive network throughput; online algorithms", } @Article{Chakrabarti:2010:NOA, author = "Amit Chakrabarti and Graham Cormode and Andrew Mcgregor", title = "A near-optimal algorithm for estimating the entropy of a stream", journal = j-TALG, volume = "6", number = "3", pages = "51:1--51:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798604", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We describe a simple algorithm for approximating the empirical entropy of a stream of $m$ values up to a multiplicative factor of $ (1 + \epsilon) $ using a single pass, {$ O(\epsilon^{ - 2} \log (\delta^{ - 1}) \log m) $} words of space, and {$ O(\log \epsilon^{ - 1} + \log \log \delta^{ - 1} + \log \log m) $} processing time per item in the stream. Our algorithm is based upon a novel extension of a method introduced by Alon et al. [1999]. This improves over previous work on this problem. We show a space lower bound of {$ \Omega (\epsilon^{ - 2} / \log^2 (\epsilon^{ - 1})) $}, demonstrating that our algorithm is near-optimal in terms of its dependency on {$ \epsilon $}.\par We show that generalizing to multiplicative-approximation of the {$k$} th-order entropy requires close to linear space for {$ k \geq 1 $}. In contrast we show that additive-approximation is possible in a single pass using only poly-logarithmic space. Lastly, we show how to compute a multiplicative approximation to the entropy of a random walk on an undirected graph.", acknowledgement = ack-nhfb, articleno = "51", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithms; Data streams; entropy", } @Article{Fattal:2010:ADM, author = "Shahar Fattal and Dana Ron", title = "Approximating the distance to monotonicity in high dimensions", journal = j-TALG, volume = "6", number = "3", pages = "52:1--52:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798605", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article we study the problem of approximating the distance of a function {$ f : [n]^d \rightarrow R $} to monotonicity where {$ [n] = \{ 1, \ldots, n \} $} and {$R$} is some fully ordered range. Namely, we are interested in randomized sublinear algorithms that approximate the Hamming distance between a given function and the closest monotone function. We allow both an additive error, parameterized by {$ \delta $}, and a multiplicative error.\par Previous work on distance approximation to monotonicity focused on the one-dimensional case and the only explicit extension to higher dimensions was with a multiplicative approximation factor exponential in the dimension {\em d}. Building on Goldreich et al. [2000] and Dodis et al. [1999], in which there are better implicit results for the case {$ n = 2 $}, we describe a reduction from the case of functions over the {$d$}-dimensional hypercube $ [n]^d $ to the case of functions over the $k$-dimensional hypercube $ [n]^k $, where $ 1 \leq k \leq d $. The quality of estimation that this reduction provides is linear in $ \lceil d / k \rceil $ and logarithmic in the size of the range {$ |R| $} (if the range is infinite or just very large, then {$ \log |R| $} can be replaced by {$ d \log n $}). Using this reduction and a known distance approximation algorithm for the one-dimensional case, we obtain a distance approximation algorithm for functions over the {$d$}-dimensional hypercube, with any range {$R$}, which has a multiplicative approximation factor of {$ O(d \log |R) $}.\par For the case of a binary range, we present algorithms for distance approximation to monotonicity of functions over one dimension, two dimensions, and the {$k$}-dimensional hypercube (for any {$ k \geq 1 $} ). Applying these algorithms and the reduction described before, we obtain a variety of distance approximation algorithms for Boolean functions over the {$d$}-dimensional hypercube which suggest a trade-off between quality of estimation and efficiency of computation. In particular, the multiplicative error ranges between {$ O(d) $} and {$ O(1) $}.", acknowledgement = ack-nhfb, articleno = "52", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "distance approximation; monotonicity; property testing; Sublinear approximation algorithms", } @Article{Martinez:2010:ASS, author = "Conrado Mart{\'\i}nez and Daniel Panario and Alfredo Viola", title = "Adaptive sampling strategies for quickselects", journal = j-TALG, volume = "6", number = "3", pages = "53:1--53:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798606", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Quickselect with median-of-3 is largely used in practice and its behavior is fairly well understood. However, the following natural adaptive variant, which we call {\em proportion-from-3}, had not been previously analyzed: ``choose as pivot the smallest of the sample if the relative rank of the sought element is below 1/3, the largest if the relative rank is above 2/3, and the median if the relative rank is between 1/3 and 2/3.'' We first analyze the average number of comparisons made when using proportion-from-2 and then for proportion-from-3. We also analyze $ \nu $-find, a generalization of proportion-from-3 with interval breakpoints at $ \nu $ and $ 1 - \nu $. We show that there exists an optimal value of $ \nu $ and we also provide the range of values of $ \nu $ where $ \nu $-find outperforms median-of-3. Then, we consider the average total cost of these strategies, which takes into account the cost of both comparisons and exchanges. Our results strongly suggest that a suitable implementation of $ \nu $-find could be the method of choice in a practical setting. We also study the behavior of proportion-from-$s$ with $ s > 3 $ and in particular we show that proportion-from-$s$-like strategies are optimal when $ s \rightarrow \infty $.", acknowledgement = ack-nhfb, articleno = "53", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Analytic combinatorics; average-case analysis; divide-and-conquer; Find; quickselect; sampling; selection", } @Article{Alon:2010:BFP, author = "Noga Alon and Shai Gutner", title = "Balanced families of perfect hash functions and their applications", journal = j-TALG, volume = "6", number = "3", pages = "54:1--54:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798607", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The construction of perfect hash functions is a well-studied topic. In this article, this concept is generalized with the following definition. We say that a family of functions from $ [n] $ to $ [k] $ is a $ \delta $-balanced $ (n, k) $-family of perfect hash functions if for every {$ S \subseteq [n] $}, {$ |S| = k $}, the number of functions that are {$1$}-{$1$} on {$S$} is between {$ T / \delta $} and {$ \delta T $} for some constant {$ T > 0 $}. The standard definition of a family of perfect hash functions requires that there will be at least one function that is {$1$}-{$1$} on {$S$}, for each {$S$} of size {$k$}. In the new notion of balanced families, we require the number of {$1$}-{$1$} functions to be almost the same (taking $ \delta $ to be close to $1$ ) for every such {$S$}. Our main result is that for any constant {$ \delta > 1 $}, a {$ \delta $}-balanced {$ (n, k) $}-family of perfect hash functions of size {$ 2^{O(k \log \log k)} \log n $} can be constructed in time {$ 2^{O(k \log \log k)} n \log n $}. Using the technique of color-coding we can apply our explicit constructions to devise approximation algorithms for various counting problems in graphs. In particular, we exhibit a deterministic polynomial-time algorithm for approximating both the number of simple paths of length {$k$} and the number of simple cycles of size {$k$} for any {$ k \leq O(\log n / \log \log \log n) $} in a graph with {$n$} vertices. The approximation is up to any fixed desirable relative error.", acknowledgement = ack-nhfb, articleno = "54", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximate counting of subgraphs; color-coding; perfect hashing", } @Article{Coppersmith:2010:OWN, author = "Don Coppersmith and Lisa K. Fleischer and Atri Rurda", title = "Ordering by weighted number of wins gives a good ranking for weighted tournaments", journal = j-TALG, volume = "6", number = "3", pages = "55:1--55:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798608", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the following simple algorithm for feedback arc set problem in weighted tournaments: order the vertices by their weighted indegrees. We show that this algorithm has an approximation guarantee of 5 if the weights satisfy {\em probability constraints\/} (for any pair of vertices $u$ and $v$, $ w_{uv} + w_{vu} = 1 $ ). Special cases of the feedback arc set problem in such weighted tournaments include the feedback arc set problem in unweighted tournaments and rank aggregation. To complement the upper bound, for any constant $ \epsilon > 0 $, we exhibit an infinite family of (unweighted) tournaments for which the aforesaid algorithm ({\em irrespective\/} of how ties are broken) has an approximation ratio of $ 5 - \epsilon $.", acknowledgement = ack-nhfb, articleno = "55", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; Borda's method; feedback arc set problem; rank aggregation; tournaments", } @Article{Gonzalez-Gutierrez:2010:ACT, author = "Arturo Gonzalez-Gutierrez and Teofilo F. Gonzalez", title = "Approximating corridors and tours via restriction and relaxation techniques", journal = j-TALG, volume = "6", number = "3", pages = "56:1--56:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798609", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a rectangular boundary partitioned into rectangles, the Minimum-Length Corridor (MLC-R) problem consists of finding a corridor of least total length. A corridor is a set of connected line segments, each of which must lie along the line segments that form the rectangular boundary and/or the boundary of the rectangles, and must include at least one point from the boundary of every rectangle and from the rectangular boundary. The MLC-R problem is known to be NP-hard. We present the first polynomial-time constant ratio approximation algorithm for the MLC-R and MLC$_k$ problems. The MLC$_k$ problem is a generalization of the MLC-R problem where the rectangles are rectilinear $c$-gons, for $ c \leq k $ and $k$ is a constant. We also present the first polynomial-time constant ratio approximation algorithm for the Group Traveling Salesperson Problem (GTSP) for a rectangular boundary partitioned into rectilinear $c$-gons as in the MLC$_k$ problem. Our algorithms are based on the restriction and relaxation approximation techniques.", acknowledgement = ack-nhfb, articleno = "56", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithms; complexity; computational geometry; Corridors; restriction and relaxation techniques", } @Article{Alber:2010:EN, author = "Susanne Alber", title = "Editorial note", journal = j-TALG, volume = "6", number = "4", pages = "57:1--57:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824778", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "57", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hajiaghayi:2010:FSI, author = "Mohammad T. Hajiaghayi and Shang-Hua Teng", title = "Foreword to special issue on {SODA 2008}", journal = j-TALG, volume = "6", number = "4", pages = "58:1--58:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824793", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "58", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ackermann:2010:CMN, author = "Marcel R. Ackermann and Johannes Bl{\"o}mer and Christian Sohler", title = "Clustering for metric and nonmetric distance measures", journal = j-TALG, volume = "6", number = "4", pages = "59:1--59:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824779", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study a generalization of the $k$-median problem with respect to an arbitrary dissimilarity measure $D$. Given a finite set $P$ of size $n$, our goal is to find a set $C$ of size $k$ such that the sum of errors $ D(P, C) = \sum_{p \in P} \min_{c \in C} D(p, c)$ is minimized. The main result in this article can be stated as follows: There exists a $ (1 + \epsilon)$-approximation algorithm for the $k$-median problem with respect to $D$, if the 1-median problem can be approximated within a factor of $ (1 + \epsilon)$ by taking a random sample of constant size and solving the 1-median problem on the sample exactly. This algorithm requires time $ n 2^O(m k \log (m k / \epsilon))$, where $m$ is a constant that depends only on $ \epsilon $ and $D$. Using this characterization, we obtain the first linear time $ (1 + \epsilon)$-approximation algorithms for the $k$-median problem in an arbitrary metric space with bounded doubling dimension, for the Kullback--Leibler divergence (relative entropy), for the Itakura-Saito divergence, for Mahalanobis distances, and for some special cases of Bregman divergences. Moreover, we obtain previously known results for the Euclidean $k$-median problem and the Euclidean $k$-means problem in a simplified manner. Our results are based on a new analysis of an algorithm of Kumar et al. [2004].", acknowledgement = ack-nhfb, articleno = "59", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Andersen:2010:LAF, author = "Reid Andersen", title = "A local algorithm for finding dense subgraphs", journal = j-TALG, volume = "6", number = "4", pages = "60:1--60:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824780", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We describe a local algorithm for finding subgraphs with high density, according to a measure of density introduced by Kannan and Vinay [1999]. The algorithm takes as input a bipartite graph $G$, a starting vertex $v$, and a parameter $k$, and outputs an induced subgraph of $G$. It is local in the sense that it does not examine the entire input graph; instead, it adaptively explores a region of the graph near the starting vertex. The running time of the algorithm is bounded by $ O(\Delta k^2)$, which depends on the maximum degree $ \Delta $, but is otherwise independent of the graph. We prove the following approximation guarantee: for any subgraph $S$ with $ k'$ vertices and density $ \theta $, there exists a set $ S' \subseteq S$ for which the algorithm outputs a subgraph with density $ \Omega (\theta / \log \Delta)$ whenever $ v \in S'$ and $ k \geq k'$. We prove that $ S'$ contains at least half of the edges in $S$.", acknowledgement = ack-nhfb, articleno = "60", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cabello:2010:FOT, author = "Sergio Cabello and Matt Devos and Jeff Erickson and Bojan Mohar", title = "Finding one tight cycle", journal = j-TALG, volume = "6", number = "4", pages = "61:1--61:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824781", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A cycle on a combinatorial surface is tight if it as short as possible in its (free) homotopy class. We describe an algorithm to compute a single tight, noncontractible, essentially simple cycle on a given orientable combinatorial surface in $ O(n \log n) $ time. The only method previously known for this problem was to compute the globally shortest noncontractible or nonseparating cycle in $ O (\min \{ g^3, n, n \log n \}) $ time, where $g$ is the genus of the surface. As a consequence, we can compute the shortest cycle freely homotopic to a chosen boundary cycle in $ O (n \log n)$ time, a tight octagonal decomposition in $ O (g n \log n)$ time, and a shortest contractible cycle enclosing a nonempty set of faces in $ O (n \log^2 n)$ time.", acknowledgement = ack-nhfb, articleno = "61", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chan:2010:BSP, author = "Timothy M. Chan", title = "On the bichromatic $k$-set problem", journal = j-TALG, volume = "6", number = "4", pages = "62:1--62:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824782", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study a generalization of the k -median problem with respect to an arbitrary dissimilarity measure D. Given a finite set P of size n, our goal is to find a set C of size k such that the sum of errors $ D(P, C) = \sum_{p \in P} \min_{c \in C} D(p, c) $ is minimized. The main result in this article can be stated as follows: There exists a $ (1 + \epsilon)$-approximation algorithm for the k median problem with respect to $D$, if the 1-median problem can be approximated within a factor of $ (1 + \epsilon)$ by taking a random sample of constant size and solving the 1-median problem on the sample exactly. This algorithm requires time $ n 2^O (m k \log (m k / \epsilon))$, where $m$ is a constant that depends only on $ \epsilon $ and $D$. Using this characterization, we obtain the first linear time $ (1 + \epsilon)$-approximation algorithms for the $k$ median problem in an arbitrary metric space with bounded doubling dimension, for the Kullback--Leibler divergence (relative entropy), for the Itakura-Saito divergence, for Mahalanobis distances, and for some special cases of Bregman divergences. Moreover, we obtain previously known results for the Euclidean $k$ median problem and the Euclidean $k$-means problem in a simplified manner. Our results are based on a new analysis of an algorithm of Kumar et al. [2004].", acknowledgement = ack-nhfb, articleno = "62", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Clarkson:2010:CSG, author = "Kenneth L. Clarkson", title = "Coresets, sparse greedy approximation, and the {Frank--Wolfe} algorithm", journal = j-TALG, volume = "6", number = "4", pages = "63:1--63:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824783", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The problem of maximizing a concave function $ f(x) $ in the unit simplex $ \Delta $ can be solved approximately by a simple greedy algorithm. For given $k$, the algorithm can find a point $ x_{(k)}$ on a $k$-dimensional face of $ \Delta $, such that $ f(x_{(k)}) \geq f(x_*) - O(1 / k)$. Here $ f(x_*)$ is the maximum value of $f$ in $ \Delta $, and the constant factor depends on $f$. This algorithm and analysis were known before, and related to problems of statistics and machine learning, such as boosting, regression, and density mixture estimation. In other work, coming from computational geometry, the existence of $ \epsilon $-coresets was shown for the minimum enclosing ball problem by means of a simple greedy algorithm. Similar greedy algorithms, which are special cases of the Frank-0Wolfe algorithm, were described for other enclosure problems. Here these results are tied together, stronger convergence results are reviewed, and several coreset bounds are generalized or strengthened.", acknowledgement = ack-nhfb, articleno = "63", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Emek:2010:NLT, author = "Yuval Emek and David Peleg and Liam Roditty", title = "A near-linear-time algorithm for computing replacement paths in planar directed graphs", journal = j-TALG, volume = "6", number = "4", pages = "64:1--64:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824784", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Let $ G = (V(G), E(G)) $ be a directed graph with nonnegative edge lengths and let $P$ be a shortest path from $s$ to $t$ in $G$. In the replacement paths problem we are required to compute for every edge $e$ in $P$, the length of a shortest path from $s$ to $t$ that avoids $e$. The fastest known algorithm for solving the problem in weighted directed graphs is the trivial one: each edge in $P$ is removed from the graph in its turn and the distance from $s$ to $t$ in the modified graph is computed. The running time of this algorithm is $ O(m n + n^2 \log n)$, where $ n = | V(G) |$ and $ m = | E(G) |$. The replacement paths problem is strongly motivated by two different applications. First, the fastest algorithm to compute the $k$ simple shortest paths from $s$ to $t$ in directed graphs [Yen 1971; Lawler 1972] repeatedly computes the replacement paths from $s$ to $t$. Its running time is $ O(k n (m + n \log n))$. Second, the computation of Vickrey pricing of edges in distributed networks can be reduced to the replacement paths problem. An open question raised by Nisan and Ronen [2001] asks whether it is possible to compute the Vickrey pricing faster than the trivial algorithm described in the previous paragraph. In this article we present a near-linear time algorithm for computing replacement paths in weighted planar directed graphs. In particular, the algorithm computes the lengths of the replacement paths in $ O (n \log^3 n)$ time (recall that in planar graphs $ m = O(n)$). This result immediately improves the running time of the two applications mentioned before by almost a linear factor. Our algorithm is obtained by combining several new ideas with a data structure of Klein [2005] that supports multisource shortest paths queries in planar directed graphs in logarithmic time. Our algorithm can be adapted to address the variant of the problem in which one is interested in the replacement path itself (rather than the length of the path). In that case the algorithm is executed in a preprocessing stage constructing a data structure that supports replacement path queries in time $ {\tilde O}(h)$, where $h$ is the number of hops in the replacement path. In addition, we can handle the variant in which vertices should be avoided instead of edges.", acknowledgement = ack-nhfb, articleno = "64", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Faigle:2010:TPG, author = "Ulrich Faigle and Britta Peis", title = "Two-phase greedy algorithms for some classes of combinatorial linear programs", journal = j-TALG, volume = "6", number = "4", pages = "65:1--65:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824785", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present greedy algorithms for some classes of combinatorial packing and cover problems within the general formal framework of Hoffman and Schwartz' lattice polyhedra. Our algorithms compute in a first phase Monge solutions for the associated dual cover and packing problems and then proceed to construct greedy solutions for the primal problems in a second phase. We show optimality of the algorithms under certain sub- and supermodular assumptions and monotone constraints. For supermodular lattice polyhedra with submodular constraints, our algorithms offer the farthest reaching generalization of Edmonds' polymatroid greedy algorithm currently known.", acknowledgement = ack-nhfb, articleno = "65", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Feldman:2010:DSS, author = "Jon Feldman and S. Muthukrishnan and Anastasios Sidiropoulos and Cliff Stein and Zoya Svitkina", title = "On distributing symmetric streaming computations", journal = j-TALG, volume = "6", number = "4", pages = "66:1--66:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824786", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A common approach for dealing with large datasets is to stream over the input in one pass, and perform computations using sublinear resources. For truly massive datasets, however, even making a single pass over the data is prohibitive. Therefore, streaming computations must be distributed over many machines. In practice, obtaining significant speedups using distributed computation has numerous challenges including synchronization, load balancing, overcoming processor failures, and data distribution. Successful systems in practice such as Google's MapReduce and Apache's Hadoop address these problems by only allowing a certain class of highly distributable tasks defined by local computations that can be applied in any order to the input. The fundamental question that arises is: How does the class of computational tasks supported by these systems differ from the class for which streaming solutions exist? We introduce a simple algorithmic model for massive, unordered, distributed (mud) computation, as implemented by these systems. We show that in principle, mud algorithms are equivalent in power to symmetric streaming algorithms. More precisely, we show that any symmetric (order-invariant) function that can be computed by a streaming algorithm can also be computed by a mud algorithm, with comparable space and communication complexity. Our simulation uses Savitch's theorem and therefore has superpolynomial time complexity. We extend our simulation result to some natural classes of approximate and randomized streaming algorithms. We also give negative results, using communication complexity arguments to prove that extensions to private randomness, promise problems, and indeterminate functions are impossible. We also introduce an extension of the mud model to multiple keys and multiple rounds.", acknowledgement = ack-nhfb, articleno = "66", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Oudot:2010:GDT, author = "Steve Y. Oudot and Leonidas J. Guibas and Jie Gao and Yue Wang", title = "Geodesic {Delaunay} triangulations in bounded planar domains", journal = j-TALG, volume = "6", number = "4", pages = "67:1--67:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824787", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce a new feature size for bounded domains in the plane endowed with an intrinsic metric. Given a point $x$ in a domain $X$, the systolic feature size of $X$ at $x$ measures half the length of the shortest loop through $x$ that is not null-homotopic in $X$. The resort to an intrinsic metric makes the systolic feature size rather insensitive to the local geometry of the domain, in contrast with its predecessors (local feature size, weak feature size, homology feature size). This reduces the number of samples required to capture the topology of $X$, provided that a reliable approximation to the intrinsic metric of $X$ is available. Under sufficient sampling conditions involving the systolic feature size, we show that the geodesic Delaunay triangulation $ D_x(L)$ of a finite sampling $L$ is homotopy equivalent to $X$. Under similar conditions, $ D_x(L)$ is sandwiched between the geodesic witness complex $ C^W_X (L)$ and a relaxed version $ C^W_{X, \nu }(L)$. In the conference version of the article, we took advantage of this fact and proved that the homology of $ D_x(L)$ (and hence the one of $X$) can be retrieved by computing the persistent homology between $ C^W_X(L)$ and $ C^W_{X, \nu }(L)$. Here, we investigate further and show that the homology of $X$ can also be recovered from the persistent homology associated with inclusions of type $ C^W_{X, \nu }(L) \hookrightarrow C^W_{X, \nu '} (L)$, under some conditions on the parameters $ \nu \leq \nu '$. Similar results are obtained for Vietoris--Rips complexes in the intrinsic metric. The proofs draw some connections with recent advances on the front of homology inference from point cloud data, but also with several well-known concepts of Riemannian (and even metric) geometry. On the algorithmic front, we propose algorithms for estimating the systolic feature size of a bounded planar domain $X$, selecting a landmark set of sufficient density, and computing the homology of $X$ using geodesic witness complexes or Rips complexes.", acknowledgement = ack-nhfb, articleno = "67", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Kapron:2010:FAB, author = "Bruce M. Kapron and David Kempe and Valerie King and Jared Saia and Vishal Sanwalani", title = "Fast asynchronous {Byzantine} agreement and leader election with full information", journal = j-TALG, volume = "6", number = "4", pages = "68:1--68:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824788", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We resolve two long-standing open problems in distributed computation by describing polylogarithmic protocols for Byzantine agreement and leader election in the asynchronous full information model with a nonadaptive malicious adversary. All past protocols for asynchronous Byzantine agreement had been exponential, and no protocol for asynchronous leader election had been known. Our protocols tolerate up to $ (1 / 3 - \epsilon) \cdot n $ faulty processors, for any positive constant $ \epsilon $. They are Monte Carlo, succeeding with probability $ 1 - o(1) $ for Byzantine agreement, and constant probability for leader election. A key technical contribution of our article is a new approach for emulating Feige's lightest bin protocol, even with adversarial message scheduling.", acknowledgement = ack-nhfb, articleno = "68", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Svitkina:2010:LBF, author = "Zoya Svitkina", title = "Lower-bounded facility location", journal = j-TALG, volume = "6", number = "4", pages = "69:1--69:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824789", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the lower-bounded facility location problem which generalizes the classical uncapacitated facility location problem in that it comes with lower bound constraints for the number of clients assigned to a facility in the case that this facility is opened. This problem was introduced independently in the papers by Karger and Minkoff [2000] and by Guha et al. [2000], both of which give bicriteria approximation algorithms for it. These bicriteria algorithms come within a constant factor of the optimal solution cost, but they also violate the lower bound constraints by a constant factor. Our result in this article is the first true approximation algorithm for the lower-bounded facility location problem which respects the lower bound constraints and achieves a constant approximation ratio for the objective function. The main technical idea for the design of the algorithm is a reduction to the capacitated facility location problem, which has known constant-factor approximation algorithms.", acknowledgement = ack-nhfb, articleno = "69", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Williams:2010:NPW, author = "Virginia Vassilevska Williams", title = "Nondecreasing paths in a weighted graph or: How to optimally read a train schedule", journal = j-TALG, volume = "6", number = "4", pages = "70:1--70:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824790", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A travel booking office has timetables giving arrival and departure times for all scheduled trains, including their origins and destinations. A customer presents a starting station and demands a route with perhaps several train connections taking him to his destination as early as possible. The booking office must find the best route for its customers. This problem was first considered in the theory of algorithms by Minty [1958], who reduced it to a problem on directed edge-weighted graphs: find a path from a given source to a given target such that the consecutive weights on the path are nondecreasing and the last weight on the path is minimized. Minty gave the first algorithm for the single-source version of the problem, in which one finds minimum last weight nondecreasing paths from the source to every other vertex. In this article we give the first linear -time algorithm for this problem in the word-RAM model of computation. We also define an all-pairs version for the problem and give a strongly polynomial truly subcubic algorithm for it. Finally, we discuss an extension of the problem in which one also has prices on trip segments and one wishes to find a cheapest valid itinerary.", acknowledgement = ack-nhfb, articleno = "70", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Agarwal:2010:HDU, author = "Pankaj K. Agarwal and Sariel Har-Peled and Micha Sharir and Yusu Wang", title = "{Hausdorff} distance under translation for points and balls", journal = j-TALG, volume = "6", number = "4", pages = "71:1--71:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824791", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the shape matching problem under the Hausdorff distance and its variants. In the first part of the article, we consider two sets $A$, $B$ of balls in $ R^d$, $ d = 2, 3$, and wish to find a translation t that minimizes the Hausdorff distance between $ A + t$, the set of all balls in $A$ shifted by $t$, and $B$. We consider several variants of this problem. First, we extend the notion of Hausdorff distance from sets of points to sets of balls, so that each ball has to be matched with the nearest ball in the other set. We also consider the problem in the standard setting, by computing the Hausdorff distance between the unions of the two sets (as point sets). Second, we consider either all possible translations $t$ (as is the standard approach), or consider only translations that keep the balls of $ A + t$ disjoint from those of $B$. We propose several exact and approximation algorithms for these problems. In the second part of the article, we note that the Hausdorff distance is sensitive to outliers, and thus consider two variants that are more robust: the root-mean-square (rms) and the summed Hausdorff distance. We propose efficient approximation algorithms for computing the minimum rms and the minimum summed Hausdorff distances under translation, between two point sets in $ R^d$. In order to obtain a fast algorithm for the summed Hausdorff distance, we propose a deterministic efficient dynamic data structure for maintaining an $ \epsilon $-approximation of the 1-median of a set of points in $ R^d$, under insertions and deletions.", acknowledgement = ack-nhfb, articleno = "71", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Carlsson:2010:FEC, author = "John Gunnar Carlsson and Benjamin Armbruster and Yinyu Ye", title = "Finding equitable convex partitions of points in a polygon efficiently", journal = j-TALG, volume = "6", number = "4", pages = "72:1--72:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824792", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Previous work has developed algorithms for finding an equitable convex partition that partitions the plane into n convex pieces each containing an equal number of red and blue points. Motivated by a vehicle routing heuristic, we look at a related problem where each piece must contain one point and an equal fraction of the area of some convex polygon. We first show how algorithms for solving the older problem lead to approximate solutions for this new equitable convex partition problem. Then we demonstrate a new algorithm that finds an exact solution to our problem in $ O (N n \log N) $ time or operations, where n is the number of points, m the number of vertices or edges of the polygon, and $ N \colon = n + m $ the sum.", acknowledgement = ack-nhfb, articleno = "72", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Rutter:2010:CLM, author = "Ignaz Rutter and Alexander Wolff", title = "Computing large matchings fast", journal = j-TALG, volume = "7", number = "1", pages = "1:1--1:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868238", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/string-matching.bib; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article we present algorithms for computing large matchings in 3-regular graphs, graphs with maximum degree 3, and 3-connected planar graphs. The algorithms give a guarantee on the size of the computed matching and take linear or slightly superlinear time. Thus they are faster than the best-known algorithm for computing maximum matchings in general graphs, which runs in $ O(\sqrt {n m}) $ time, where $n$ denotes the number of vertices and $m$ the number of edges of the given graph. For the classes of 3-regular graphs and graphs with maximum degree 3, the bounds we achieve are known to be best possible. We also investigate graphs with block trees of bounded degree, where the $d$-block tree is the adjacency graph of the $d$-connected components of the given graph. In 3-regular graphs and 3-connected planar graphs with bounded-degree 2- and 4-block trees, respectively, we show how to compute maximum matchings in slightly superlinear time.", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Iwama:2010:AAS, author = "Kazuo Iwama and Shuichi Miyazaki and Hiroki Yanagisawa", title = "Approximation algorithms for the sex-equal stable marriage problem", journal = j-TALG, volume = "7", number = "1", pages = "2:1--2:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868239", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The stable marriage problem is a classical matching problem introduced by Gale and Shapley. It is known that for any instance, there exists a solution, and there is a polynomial time algorithm to find one. However, the matching obtained by this algorithm is man-optimal, that is, the matching is favorable for men but unfavorable for women, (or, if we exchange the roles of men and women, the resulting matching is woman-optimal). The sex-equal stable marriage problem, posed by Gusfield and Irving, seeks a stable matching ``fair'' for both genders. Specifically it seeks a stable matching with the property that the sum of the men's scores is as close as possible to that of the women's. This problem is known to be strongly NP-hard. In this paper, we give a polynomial time algorithm for finding a near optimal solution for the sex-equal stable marriage problem. Furthermore, we consider the problem of optimizing an additional criterion: among stable matchings that are near optimal in terms of the sex-equality, find a minimum egalitarian stable matching. We show that this problem is strongly NP-hard, and give a polynomial time algorithm whose approximation ratio is less than two.", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Djidjev:2010:FAC, author = "Hristo N. Djidjev", title = "A faster algorithm for computing the girth of planar and bounded genus graphs", journal = j-TALG, volume = "7", number = "1", pages = "3:1--3:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868240", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The girth of a graph $G$ is the length of a shortest cycle of $G$. In this article we design an $ O(n^{5 / 4} \log n)$ algorithm for finding the girth of an undirected $n$-vertex planar graph, the first $ o(n^2)$ algorithm for this problem. We also extend our results for the class of graphs embedded into an orientable surface of small genus. Our approach uses several techniques such as graph partitioning, hammock decomposition, graph covering, and dynamic shortest-path computation. We discuss extensions and generalizations of our result.", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Baier:2010:LBC, author = "Georg Baier and Thomas Erlebach and Alexander Hall and Ekkehard K{\"o}hler and Petr Kolman and Ondrej Pangr{\'a}c and Heiko Schilling and Martin Skutella", title = "Length-bounded cuts and flows", journal = j-TALG, volume = "7", number = "1", pages = "4:1--4:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868241", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "For a given number $L$, an $L$-length-bounded edge-cut (node-cut, respectively) in a graph $G$ with source $s$ and sink $t$ is a set $C$ of edges (nodes, respectively) such that no $s$--$t$-path of length at most $L$ remains in the graph after removing the edges (nodes, respectively) in $C$. An $L$-length-bounded flow is a flow that can be decomposed into flow paths of length at most $L$. In contrast to classical flow theory, we describe instances for which the minimum $L$-length-bounded edge-cut (node-cut, respectively) is $ \Theta (n^{2 / 3})$-times $ (\Theta (\sqrt {n}))$-times, respectively larger than the maximum $L$ length-bounded flow, where n denotes the number of nodes; this is the worst case. We show that the minimum length-bounded cut problem is NP -hard to approximate within a factor of $ 1.1377$ for $ L \geq 5$ in the case of node-cuts and for $ L \geq 4$ in the case of edge-cuts. We also describe algorithms with approximation ratio $ O(\min \{ L, n / L \}) \subseteq O (\sqrt {n})$ in the node case and $ O (\min \{ L, n^2 / L^2, \sqrt {m} \}) \subseteq O(n^{2 / 3})$ in the edge case, where $m$ denotes the number of edges. Concerning $L$ length-bounded flows, we show that in graphs with unit-capacities and general edge lengths it is NP complete to decide whether there is a fractional length-bounded flow of a given value. We analyze the structure of optimal solutions and present further complexity results.", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Baswana:2010:ASS, author = "Surender Baswana and Telikepalli Kavitha and Kurt Mehlhorn and Seth Pettie", title = "Additive spanners and $ (\alpha, \beta)$-spanners", journal = j-TALG, volume = "7", number = "1", pages = "5:1--5:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868242", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "An $ (\alpha, \beta)$-spanner of an unweighted graph $G$ is a subgraph $H$ that distorts distances in $G$ up to a multiplicative factor of $ \alpha $ and an additive term $ \beta $. It is well known that any graph contains a (multiplicative) $ (2 k - 1, 0)$-spanner of size $ O (n^{1 + 1 / k})$ and an (additive) $ (1, 2)$-spanner of size $ O (n^{3 / 2})$. However no other additive spanners are known to exist. In this article we develop a couple of new techniques for constructing $ (\alpha, \beta)$-spanners. Our first result is an additive (1,6)-spanner of size $ O (n^{4 / 3})$. The construction algorithm can be understood as an economical agent that assigns costs and values to paths in the graph, purchasing affordable paths and ignoring expensive ones, which are intuitively well approximated by paths already purchased. We show that this path buying algorithm can be parameterized in different ways to yield other sparseness-distortion tradeoffs. Our second result addresses the problem of which $ (\alpha, \beta)$-spanners can be computed efficiently, ideally in linear time. We show that, for any $k$, a $ (k, k - 1)$-spanner with size $ O (k n^{1 + 1 / k})$ can be found in linear time, and, further, that in a distributed network the algorithm terminates in a constant number of rounds. Previous spanner constructions with similar performance had roughly twice the multiplicative distortion.", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Flammini:2010:BSP, author = "Michele Flammini and Gaia Nicosia", title = "On the bicriteria $k$-server problem", journal = j-TALG, volume = "7", number = "1", pages = "6:1--6:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868244", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article we consider multicriteria formulations of classical online problems in which an algorithm must simultaneously perform well with respect to two different cost measures. Every strategy for serving a sequence of requests is characterized by a pair of costs and therefore there can be many different minimal or optimal incomparable solutions. The adversary is assumed to choose from one of these minimal strategies and the performance of the algorithm is measured with respect to the costs the adversary pays servicing the sequence according to its determined choice of strategy. We consider a parametric family of functions which includes all the possible selections for such strategies. Then, starting from a simple general method that combines any multicriteria instance into a single-criterion one, we provide a universal multicriteria algorithm that can be applied to different online problems. In the multicriteria k-server formulation with two different edge weightings, for each function class, such a universal algorithm achieves competitive ratios that are only an O (log W) multiplicative factor away from the corresponding determined lower bounds, where W is the maximum ratio between the two weights associated to each edge. We then extend our results to two specific functions, for which nearly optimal competitive algorithms are obtained by exploiting more knowledge of the selection properties. Finally, we show how to apply our framework to other multicriteria online problems sharing similar properties.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Epstein:2010:OUC, author = "Leah Epstein and Rob {Van Stee}", title = "On the online unit clustering problem", journal = j-TALG, volume = "7", number = "1", pages = "7:1--7:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868245", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We continue the study of the online unit clustering problem, introduced by Chan and Zarrabi-Zadeh ( Workshop on Approximation and Online Algorithms 2006, LNCS 4368, p. 121--131. Springer, 2006). We design a deterministic algorithm with a competitive ratio of 7/4 for the one-dimensional case. This is the first deterministic algorithm that beats the bound of 2. It also has a better competitive ratio than the previous randomized algorithms. Moreover, we provide the first non-trivial deterministic lower bound, improve the randomized lower bound, and prove the first lower bounds for higher dimensions.", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gao:2010:CLH, author = "Jie Gao and Michael Langberg and Leonard J. Schulman", title = "Clustering lines in high-dimensional space: Classification of incomplete data", journal = j-TALG, volume = "7", number = "1", pages = "8:1--8:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868246", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A set of k balls B$_1$, \ldots{}, B$_k$ in a Euclidean space is said to cover a collection of lines if every line intersects some ball. We consider the k --- center problem for lines in high-dimensional space: Given a set of n lines $^l$ = { l$_1$,\ldots{}, l$_n$ in R$^d$, find k balls of minimum radius which cover l. We present a 2-approximation algorithm for the cases k = 2, 3 of this problem, having running time quasi-linear in the number of lines and the dimension of the ambient space. Our result for 3-clustering is strongly based on a new result in discrete geometry that may be of independent interest: a Helly-type theorem for collections of axis-parallel ``crosses'' in the plane. The family of crosses does not have finite Helly number in the usual sense. Our Helly theorem is of a new type: it depends on $ \epsilon $-contracting the sets. In statistical practice, data is often incompletely specified; we consider lines as the most elementary case of incompletely specified data points. Clustering of data is a key primitive in nonparametric statistics. Our results provide a way of performing this primitive on incomplete data, as well as imputing the missing values.}", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cook:2010:GFD, author = "Atlas F. {Cook IV} and Carola Wenk", title = "Geodesic {Fr{\'e}chet} distance inside a simple polygon", journal = j-TALG, volume = "7", number = "1", pages = "9:1--9:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868247", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present an alternative to parametric search that applies to both the nongeodesic and geodesic Fr{\'e}chet optimization problems. This randomized approach is based on a variant of red-blue intersections and is appealing due to its elegance and practical efficiency when compared to parametric search. We introduce the first algorithm to compute the geodesic Fr{\'e}chet distance between two polygonal curves A and B inside a simple bounding polygon P. The geodesic Fr{\'e}chet decision problem is solved almost as fast as its nongeodesic sibling in $ O (N^2 \log k) $ time and $ O (k + N) $ space after $ O(k) $ preprocessing, where $N$ is the larger of the complexities of $A$ and $B$ and $k$ is the complexity of $P$. The geodesic Fr{\'e}chet optimization problem is solved by a randomized approach in $ O (k + N^2 \log k N \log N)$ expected time and $ O (k + N^2)$ space. This runtime is only a logarithmic factor larger than the standard nongeodesic Fr{\'e}chet algorithm [Alt and Godau 1995]. Results are also presented for the geodesic Fr{\'e}chet distance in a polygonal domain with obstacles and the geodesic Hausdorff distance for sets of points or sets of line segments inside a simple polygon P.", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ferragina:2010:CPI, author = "Paolo Ferragina and Rossano Venturini", title = "The compressed permuterm index", journal = j-TALG, volume = "7", number = "1", pages = "10:1--10:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868248", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The Permuterm index [Garfield 1976] is a time-efficient and elegant solution to the string dictionary problem in which pattern queries may possibly include one wild-card symbol (called Tolerant Retrieval problem). Unfortunately the Permuterm index is space inefficient because it quadruples the dictionary size. In this article we propose the Compressed Permuterm Index which solves the Tolerant Retrieval problem in time proportional to the length of the searched pattern, and space close to the $k$ th order empirical entropy of the indexed dictionary. We also design a dynamic version of this index that allows to efficiently manage insertion in, and deletion from, the dictionary of individual strings. The result is based on a simple variant of the Burrows--Wheeler Transform, defined on a dictionary of strings of variable length, that allows to efficiently solve the Tolerant Retrieval problem via known (dynamic) compressed indexes [Navarro and M{\"a}kinen 2007]. We will complement our theoretical study with a significant set of experiments that show that the Compressed Permuterm Index supports fast queries within a space occupancy that is close to the one achievable by compressing the string dictionary via gzip or bzip. This improves known approaches based on Front-Coding [Witten et al. 1999] by more than 50\% in absolute space occupancy, still guaranteeing comparable query time.", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Agarwal:2010:EBU, author = "Pankaj K. Agarwal and Lars Arge and Ke Yi", title = "{I/O}-efficient batched union--find and its applications to terrain analysis", journal = j-TALG, volume = "7", number = "1", pages = "11:1--11:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868249", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article we present an I/O-efficient algorithm for the batched (off-line) version of the union-find problem. Given any sequence of $N$ union and find operations, where each union operation joins two distinct sets, our algorithm uses $ O (\SORT (N)) = O (\frac N B \log_{M / B} \frac N B)$ I/Os, where $M$ is the memory size and $B$ is the disk block size. This bound is asymptotically optimal in the worst case. If there are union operations that join a set with itself, our algorithm uses $ O (\SORT (N) + \MST (N))$ I/Os, where $ \MST (N)$ is the number of I/Os needed to compute the minimum spanning tree of a graph with N edges. We also describe a simple and practical $ O (\SORT (N) \log (\frac N M))$-I/O algorithm for this problem, which we have implemented. We are interested in the union-find problem because of its applications in terrain analysis. A terrain can be abstracted as a height function defined over $ R^2$, and many problems that deal with such functions require a union-find data structure. With the emergence of modern mapping technologies, huge amount of elevation data is being generated that is too large to fit in memory, thus I/O-efficient algorithms are needed to process this data efficiently. In this article, we study two terrain-analysis problems that benefit from a union-find data structure: (i) computing topological persistence and (ii) constructing the contour tree. We give the first $ O(\SORT (N))$-I/O algorithms for these two problems, assuming that the input terrain is represented as a triangular mesh with $N$ vertices.", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Goel:2010:HPE, author = "Ashish Goel and Sudipto Guha and Kamesh Munagala", title = "How to probe for an extreme value", journal = j-TALG, volume = "7", number = "1", pages = "12:1--12:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868250", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In several systems applications, parameters such as load are known only with some associated uncertainty, which is specified, or modeled, as a distribution over values. The performance of the system optimization and monitoring schemes can be improved by spending resources such as time or bandwidth in observing or resolving the values of these parameters. In a resource-constrained situation, deciding which parameters to observe in order to best optimize the expected system performance (or in general, optimize the expected value of a certain objective function) itself becomes an interesting optimization problem. In this article, we initiate the study of such problems that we term ``model-driven optimization''. In particular, we study the problem of optimizing the minimum value in the presence of observable distributions. We show that this problem is NP-Hard, and present greedy algorithms with good performance bounds. The proof of the performance bounds are via novel sub-modularity arguments and connections to covering integer programs.", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Caragiannis:2010:TLA, author = "Ioannis Caragiannis and Christos Kaklamanis and Panagiotis Kanellopoulos", title = "Taxes for linear atomic congestion games", journal = j-TALG, volume = "7", number = "1", pages = "13:1--13:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868251", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study congestion games where players aim to access a set of resources. Each player has a set of possible strategies and each resource has a function associating the latency it incurs to the players using it. Players are non--cooperative and each wishes to follow a strategy that minimizes her own latency with no regard to the global optimum. Previous work has studied the impact of this selfish behavior on system performance. In this article, we study the question of how much the performance can be improved if players are forced to pay taxes for using resources. Our objective is to extend the original game so that selfish behavior does not deteriorate performance. We consider atomic congestion games with linear latency functions and present both negative and positive results. Our negative results show that optimal system performance cannot be achieved even in very simple games. On the positive side, we show that there are ways to assign taxes that can improve the performance of linear congestion games by forcing players to follow strategies where the total latency suffered is within a factor of 2 of the minimum possible; this result is shown to be tight. Furthermore, even in cases where in the absence of taxes the system behavior may be very poor, we show that the total disutility of players (latency plus taxes) is not much larger than the optimal total latency. Besides existential results, we show how to compute taxes in time polynomial in the size of the game by solving convex quadratic programs. Similar questions have been extensively studied in the model of non-atomic congestion games. To the best of our knowledge, this is the first study of the efficiency of taxes in atomic congestion games.", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Georgiadis:2011:DSM, author = "Loukas Georgiadis and Haim Kaplan and Nira Shafrir and Robert E. Tarjan and Renato F. Werneck", title = "Data structures for mergeable trees", journal = j-TALG, volume = "7", number = "2", pages = "14:1--14:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921660", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Motivated by an application in computational geometry, we consider a novel variant of the problem of efficiently maintaining a forest of dynamic rooted trees. This variant includes an operation that merges two tree paths. In contrast to the standard problem, in which a single operation can only add or delete one arc, one merge can add and delete up to a linear number of arcs. In spite of this, we develop three different methods that need only polylogarithmic time per operation. The first method extends a solution of Farach and Thorup [1998] for the special case of paths. Each merge takes {$ O(\log^2 n) $} amortized time on an {$n$}-node forest and each standard dynamic tree operation takes {$ O(\log n) $} time; the latter bound is amortized, worst case, or randomized depending on the underlying data structure. For the special case that occurs in the motivating application, in which arbitrary arc deletions (cuts) do not occur, we give a method that takes {$ O(\log n) $} time per operation, including merging. This is best possible in a model of computation with an {$ \Omega (n \log n) $} lower bound for sorting {$n$} numbers, since such sorting can be done in {$ O(n) $} tree operations. For the even-more-special case in which there are no cuts and no parent queries, we give a method that uses standard dynamic trees as a black box: each mergeable tree operation becomes a constant number of standard dynamic tree operations. This third method can also be used in the motivating application, but only by changing the algorithm in the application. Each of our three methods needs different analytical tools and reveals different properties of dynamic trees.", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chakaravarthy:2011:DTE, author = "Venkatesan T. Chakaravarthy and Vinayaka Pandit and Sambuddha Roy and Pranjal Awasthi and Mukesh K. Mohania", title = "Decision trees for entity identification: {Approximation} algorithms and hardness results", journal = j-TALG, volume = "7", number = "2", pages = "15:1--15:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921661", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problem of constructing decision trees for entity identification from a given relational table. The input is a table containing information about a set of entities over a fixed set of attributes and a probability distribution over the set of entities that specifies the likelihood of the occurrence of each entity. The goal is to construct a decision tree that identifies each entity unambiguously by testing the attribute values such that the average number of tests is minimized. This classical problem finds such diverse applications as efficient fault detection, species identification in biology, and efficient diagnosis in the field of medicine. Prior work mainly deals with the special case where the input table is binary and the probability distribution over the set of entities is uniform. We study the general problem involving arbitrary input tables and arbitrary probability distributions over the set of entities. We consider a natural greedy algorithm and prove an approximation guarantee of {$ O(r_K \cdot \log N) $}, where {$N$} is the number of entities and {$K$} is the maximum number of distinct values of an attribute. The value {$ r_K $} is a suitably defined Ramsey number, which is at most {$ \log K $}. We show that it is NP-hard to approximate the problem within a factor of {$ \Omega (\log N) $}, even for binary tables (i.e., {$ K = 2 $}). Thus, for the case of binary tables, our approximation algorithm is optimal up to constant factors (since {$ r_2 = 2 $}). In addition, our analysis indicates a possible way of resolving a Ramsey-theoretic conjecture by Erd{\H{o}}s.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Jacobs:2011:CFA, author = "Tobias Jacobs", title = "Constant factor approximations for the hotlink assignment problem", journal = j-TALG, volume = "7", number = "2", pages = "16:1--16:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921662", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The concept of hotlink assignment aims at reducing the navigation effort for the users of a Web directory or similar structure by inserting a limited number of additional hyperlinks called hotlinks. The $k$-hotlink assignment problem denotes the task of adding at most $k$ outgoing hotlinks to each page of a tree-like site, minimizing the path length, that is, the expected number of ``clicks'' necessary for the user to reach her destination page. Another common formulation of this problem is to maximize the gain, that is, the path length reduction achieved by the assignment. In this work we analyze the natural greedy strategy, proving that it reaches the optimal gain up to the constant factor of 2. Considering the gain, we also prove the existence of a PTAS. Finally, we give a polynomial-time 2-approximation for the 1-hotlink assignment problem, which constitutes the first constant factor approximation in terms of the path length. The algorithms' performance analyses are made possible by a set of three new basic operations for the transformation of hotlink assignments.", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ambuhl:2011:TEL, author = "Christoph Amb{\"u}hl and Leszek Gasieniec and Andrzej Pelc and Tomasz Radzik and Xiaohui Zhang", title = "Tree exploration with logarithmic memory", journal = j-TALG, volume = "7", number = "2", pages = "17:1--17:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921663", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the task of network exploration by a mobile agent (robot) with small memory. The agent has to traverse all nodes and edges of a network (represented as an undirected connected graph), and return to the starting node. Nodes of the network are unlabeled and edge ports are locally labeled at each node. The agent has no a priori knowledge of the topology of the network or of its size, and cannot mark nodes in any way. Under such weak assumptions, cycles in the network may prevent feasibility of exploration, hence we restrict attention to trees. We present an algorithm to accomplish tree exploration (with return) using {$ O(\log n) $}-bit memory for all {$n$}-node trees. This strengthens the result from Diks et al. [2004], where {$ O(\log^2 n) $}-bit memory was used for tree exploration, and matches the lower bound on memory size proved there. We also extend our {$ O(\log n) $}-bit memory traversal mechanism to a weaker model in which ports at each node are ordered in circular manner, however, the explicit values of port numbers are not available.", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chekuri:2011:SCP, author = "Chandra Chekuri and Guy Even and Anupam Gupta and Danny Segev", title = "Set connectivity problems in undirected graphs and the directed {Steiner} network problem", journal = j-TALG, volume = "7", number = "2", pages = "18:1--18:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921664", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the generalized connectivity problem, we are given an edge-weighted graph {$ G = (V, E) $} and a collection {$ D = \{ (S_1, T_1), \ldots {}, (S_k, T_k) \} $} of distinct demands each demand {$ (S_i, T_i) $} is a pair of disjoint vertex subsets. We say that a subgraph {$F$} of {$G$} connects a demand {$ (S_i, T_i) $} when it contains a path with one endpoint in {$ S_i $} and the other in {$ T_i $}. The goal is to identify a minimum weight subgraph that connects all demands in D. Alon et al. (SODA '04) introduced this problem to study online network formation settings and showed that it captures some well-studied problems such as Steiner forest, facility location with nonmetric costs, tree multicast, and group Steiner tree. Obtaining a nontrivial approximation ratio for generalized connectivity was left as an open problem. We describe the first poly-logarithmic approximation algorithm for generalized connectivity that has a performance guarantee of {$ O(\log^2 n \log^2 k) $}. Here, {$n$} is the number of vertices in {$G$} and {$k$} is the number of demands. We also prove that the cut-covering relaxation of this problem has an {$ O(\log^3 n \log^2 k) $} integrality gap. Building upon the results for generalized connectivity, we obtain improved approximation algorithms for two problems that contain generalized connectivity as a special case. For the directed Steiner network problem, we obtain an {$ O(k^{1 / 2 + \epsilon }) $} approximation which improves on the currently best performance guarantee of {$ \tilde {O}(k^{2 / 3}) $} due to Charikar et al. (SODA '98). For the set connector problem, recently introduced by Fukunaga and Nagamochi (IPCO '07), we present a poly-logarithmic approximation; this result improves on the previously known ratio which can be {$ \Omega (n) $} in the worst case.", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{DeVerdiere:2011:SVD, author = "{\'E}ric Colin {De Verdi{\`e}re} and Alexander Schrijver", title = "Shortest vertex-disjoint two-face paths in planar graphs", journal = j-TALG, volume = "7", number = "2", pages = "19:1--19:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921665", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Let {$G$} be a directed planar graph of complexity {$n$}, each arc having a nonnegative length. Let {$s$} and {$t$} be two distinct faces of {$G$} let {$ s_1, \ldots {}, s_k $} be vertices incident with {$s$} let {$ t_1, \ldots {}, t_k $} be vertices incident with $t$. We give an algorithm to compute $k$ pairwise vertex-disjoint paths connecting the pairs $ (s_i, t_i) $ in {$G$}, with minimal total length, in {$ O(k n \log n) $} time.", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Elkin:2011:SFD, author = "Michael Elkin", title = "Streaming and fully dynamic centralized algorithms for constructing and maintaining sparse spanners", journal = j-TALG, volume = "7", number = "2", pages = "20:1--20:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921666", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a streaming algorithm for constructing sparse spanners and show that our algorithm significantly outperforms the state-of-the-art algorithm for this task (due to Feigenbaum et al.). Specifically, the processing time per edge of our algorithm is {$ O(1) $}, and it is drastically smaller than that of the algorithm of Feigenbaum et al., and all other efficiency parameters of our algorithm are no greater (and some of them are strictly smaller) than the respective parameters of the state-of-the-art algorithm. We also devise a fully dynamic centralized algorithm maintaining sparse spanners. This algorithm has incremental update time of {$ O(1) $}, and a nontrivial decremental update time. To our knowledge, this is the first fully dynamic centralized algorithm for maintaining sparse spanners that provides nontrivial bounds on both incremental and decremental update time for a wide range of stretch parameter {$t$}.", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cormode:2011:ADF, author = "Graham Cormode and S. Muthukrishnan and Ke Yi", title = "Algorithms for distributed functional monitoring", journal = j-TALG, volume = "7", number = "2", pages = "21:1--21:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921667", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Consider the following problem: We have $k$ players each receiving a stream of items, and communicating with a central coordinator. Let the multiset of items received by player $i$ up until time $t$ be {$ A_i(t) $}. The coordinator's task is to monitor a given function {$f$} computed over the union of the inputs {$ \cup_i A_i(t) $}, continuously at all times {$t$}. The goal is to minimize the number of bits communicated between the players and the coordinator. Of interest is the approximate version where the coordinator outputs {$1$} if {$ f \geq \tau $} and $0$ if $ f \leq (1 - \epsilon) \tau $. This defines the $ (k, f, \tau, \epsilon) $ distributed functional monitoring problem. Functional monitoring problems are fundamental in distributed systems, in particular sensor networks, where we must minimize communication; they also connect to the well-studied streaming model and communication complexity. Yet few formal bounds are known for functional monitoring. We give upper and lower bounds for the $ (k, f, \tau, \epsilon) $ problem for some of the basic $f$'s. In particular, we study the frequency moments F$_p$ for $ p = 0, 1, 2 $. For {$ F_0 $} and {$ F_1 $}, we obtain monitoring algorithms with cost almost the same as algorithms that compute the function for a single instance of time. However, for {$ F_2 $} the monitoring problem seems to be much harder than computing the function for a single time instance. We give a carefully constructed multiround algorithm that uses ``sketch summaries'' at multiple levels of details and solves the {$ (k, F_2, \tau, \epsilon) $} problem with communication {$ \tilde {O} (k^2 / \epsilon + k^{3 / 2} / \epsilon^3) $}. Our algorithmic techniques are likely to be useful for other functional monitoring problems as well.", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Halldorsson:2011:SEC, author = "Magn{\'u}s M. Halld{\'o}rsson and Guy Kortsarz and Maxim Sviridenko", title = "Sum edge coloring of multigraphs via configuration {LP}", journal = j-TALG, volume = "7", number = "2", pages = "22:1--22:21", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921668", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the scheduling of biprocessor jobs under sum objective (BPSMSM). Given a collection of unit-length jobs where each job requires the use of two processors, find a schedule such that no two jobs involving the same processor run concurrently. The objective is to minimize the sum of the completion times of the jobs. Equivalently, we would like to find a sum edge coloring of a given multigraph, that is, a partition of its edge set into matchings {$ M_1 $}, \ldots {}, {$ M_t $} minimizing {$ \Sigma_{i = 1}^t i |M_i| $}.\par This problem is APX-hard, even in the case of bipartite graphs [Marx 2009]. This special case is closely related to the classic open shop scheduling problem. We give a 1.8298-approximation algorithm for BPSMSM improving the previously best ratio known of 2 [Bar-Noy et al. 1998]. The algorithm combines a configuration LP with greedy methods, using nonstandard randomized rounding on the LP fractions. We also give an efficient combinatorial 1.8886-approximation algorithm for the case of simple graphs, which gives an improved {$ 1.79568 + O(\log \bar {d} / \bar {d}) $}-approximation in graphs of large average degree {$ \bar {d} $}.", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ben-Aroya:2011:CAF, author = "Avraham Ben-Aroya and Sivan Toledo", title = "Competitive analysis of flash memory algorithms", journal = j-TALG, volume = "7", number = "2", pages = "23:1--23:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921669", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Flash memories are widely used in computer systems ranging from embedded systems to workstations and servers to digital cameras and mobile phones. The memory cells of flash devices can only endure a limited number of write cycles, usually between 10,000 and 1,000,000. Furthermore, cells containing data must be erased before they can store new data, and erasure operations erase large blocks of memory, not individual cells. To maximize the endurance of the device (the amount of useful data that can be written to it before one of its cells wears out), flash-based systems move data around in an attempt to reduce the total number of erasures and to level the wear of the different erase blocks. This data movement introduces an interesting online problem called the wear-leveling problem. Wear-leveling algorithms have been used at least since 1993, but they have never been mathematically analyzed. In this article we analyze the two main wear-leveling problems. We show that a simple randomized algorithm for one of them is essentially optimal both in the competitive sense and in the absolute sense (our competitive result relies on an analysis of a nearly-optimal offline algorithm). We show that deterministic algorithms cannot achieve comparable endurance. We also analyze a more difficult problem and show that offline algorithms for it can improve upon naive approaches, but that online algorithms essentially cannot.", acknowledgement = ack-nhfb, articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Aumann:2011:FWP, author = "Yonatan Aumann and Moshe Lewenstein and Noa Lewenstein and Dekel Tsur", title = "Finding witnesses by peeling", journal = j-TALG, volume = "7", number = "2", pages = "24:1--24:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921670", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the $k$-matches problem, we are given a pattern and a text, and for each text location, the desired output consists of all aligned matching characters if there are $k$ or fewer of them, and any $k$ aligned matching characters if there are more than $k$ of them. This problem is one of several string matching problems that seek not only to find where the pattern matches the text under different ``match'' definitions, but also to provide witnesses to the match. Other such problems include $k$-aligned ones, $k$-witnesses, and $k$-mismatches. In addition, the solutions to several other string matching problems rely on the efficient solutions of the witness finding problems. In this article we provide a general method for solving such witness finding problems efficiently. We do so by casting the problem as a generalization of group testing, which we then solve by a process we call peeling. Using this general framework we obtain improved results for all of the problems mentioned. We also show that our method also solves a couple of problems outside the pattern matching domain.", acknowledgement = ack-nhfb, articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Choi:2011:CPM, author = "Yongwook Choi and Wojciech Szpankowski", title = "Constrained pattern matching", journal = j-TALG, volume = "7", number = "2", pages = "25:1--25:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921671", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Constrained sequences are strings satisfying certain additional structural restrictions (e.g., some patterns are forbidden). They find applications in communication, digital recording, and biology. In this article, we restrict our attention to the so-called $ (d, k) $ constrained binary sequences in which any run of zeros must be of length at least $d$ and at most $k$, where $ 0 \leq d < k $. In many applications, one needs to know the number of occurrences of a given pattern $w$ in such sequences, for which we coin the term constrained pattern matching. For a given word $w$, we first estimate the mean and the variance of the number of occurrences of $w$ in a $ (d, k) $ sequence generated by a memoryless source. Then we present the central limit theorem and large deviations results. As a by-product, we enumerate asymptotically the number of $ (d, k) $ sequences with exactly $r$ occurrences of $w$, and compute Shannon entropy of $ (d, k) $ sequences with a given number of occurrences of $w$. We also apply our results to detect under- and overrepresented patterns in neuronal data (spike trains), which satisfy structural constraints that match the framework of $ (d, k) $ binary sequences. Throughout this article we use techniques of analytic combinatorics such as combinatorial calculus, generating functions, and complex asymptotics.", acknowledgement = ack-nhfb, articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Fu:2011:DAH, author = "Bin Fu and Ming-Yang Kao and Lusheng Wang", title = "Discovering almost any hidden motif from multiple sequences", journal = j-TALG, volume = "7", number = "2", pages = "26:1--26:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921672", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study a natural probabilistic model for motif discovery. In this model, there are $k$ background sequences, and each character in a background sequence is a random character from an alphabet {$ \Sigma $}. A motif {$ G = g_1, g_2, \ldots {}, g_m $} is a string of {$m$} characters. Each background sequence is implanted with a probabilistically generated approximate copy of {$G$}. For a probabilistically generated approximate copy {$ b_1, b_2, \ldots {}, b_m $} of {$G$}, every character is probabilistically generated such that the probability for {$ b_i \neq g_i $} is at most {$ \alpha $}. In this article, we develop an efficient algorithm that can discover a hidden motif from a set of sequences for any alphabet {$ \Sigma $} with {$ | \Sigma | \geq 2 $} and is applicable to DNA motif discovery. We prove that for {$ \alpha < 1 / 8 (1 - 1 / | \Sigma |) $}, there exist positive constants {$ c_0 $}, {$ \epsilon $}, and {$ \delta_2 $} such that if there are at least $ c_0 \log n $ input sequences, then in {$ O(n^2 / h (\log n)^{O(1)}) $} time this algorithm finds the motif with probability at least {$ 3 / 4 $} for every {$ G \in \Sigma^\rho - \Psi_{\rho, h, \epsilon }(\Sigma) $}, where {$n$} the length of longest sequences, {$ \rho $} is the length of the motif, {$h$} is a parameter with $ \rho \geq 4 h \geq \delta_2 \log n $, and {$ \Psi_{\rho, h, \epsilon }(\Sigma) $} is a small subset of at most {$ 2^{ - \Theta (\epsilon^2 h)} $} fraction of the sequences in {$ \Sigma^\rho $}.", acknowledgement = ack-nhfb, articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Nong:2011:CIS, author = "Ge Nong and Sen Zhang and Wai Hong Chan", title = "Computing the {Inverse Sort Transform} in linear time", journal = j-TALG, volume = "7", number = "2", pages = "27:1--27:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921673", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The Sort Transform (ST) can significantly speed up the block sorting phase of the Burrows-Wheeler Transform (BWT) by sorting the limited order contexts. However, the best result obtained so far for the inverse ST has a time complexity {$ O(N \log k) $} and a space complexity {$ O(N) $}, where {$N$} and {$k$} are the text size and the context order of the transform, respectively. In this article, we present a novel algorithm that can compute the inverse ST for any {$k$}-order contexts in an {$ O(N) $} time and space complexity, a linear result independent of {$k$}. The main idea behind the design of this linear algorithm is a set of cycle properties of {$k$}-order contexts that we explore for this work. These newly discovered cycle properties allow us to quickly compute the Longest Common Prefix (LCP) between any pair of adjacent {$k$}-order contexts that may belong to two different cycles, which eventually leads to the proposed linear-time solution.", acknowledgement = ack-nhfb, articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Friggstad:2011:MMM, author = "Zachary Friggstad and Mohammad R. Salavatipour", title = "Minimizing movement in mobile facility location problems", journal = j-TALG, volume = "7", number = "3", pages = "28:1--28:??", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978783", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the mobile facility location problem, which is a variant of the classical facility location, each facility and client is assigned to a start location in a metric graph and our goal is to find a destination node for each client and facility such that every client is sent to a node which is the destination of some facility. The quality of a solution can be measured either by the total distance clients and facilities travel or by the maximum distance traveled by any client or facility. As we show in this article (by an approximation-preserving reduction), the problem of minimizing the total movement of facilities and clients generalizes the classical $k$-median problem. The class of movement problems was introduced by Demaine et al. [2007] where a simple 2-approximation was proposed for the minimum maximum movement mobile facility location problem while an approximation for the minimum total movement variant and hardness results for both were left as open problems. Our main result here is an 8-approximation algorithm for the minimum total movement mobile facility location problem. Our algorithm is obtained by rounding an LP relaxation in five phases. For the minimum maximum movement mobile facility location problem, we show that we cannot have a better than a 2-approximation for the problem, unless P = NP so the simple algorithm proposed by Demaine et al. [2007] is essentially best possible.", acknowledgement = ack-nhfb, articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Borodin:2011:HWC, author = "Allan Borodin and David Cashman and Avner Magen", title = "How well can primal-dual and local-ratio algorithms perform?", journal = j-TALG, volume = "7", number = "3", pages = "29:1--29:??", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978784", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We define an algorithmic paradigm, the stack model, that captures many primal-dual and local-ratio algorithms for approximating covering and packing problems. The stack model is defined syntactically and without any complexity limitations and hence our approximation bounds are independent of the P versus NP question. Using the stack model, we bound the performance of a broad class of primal-dual and local-ratio algorithms and supply a $ (\log n + 1) / 2 $ inapproximability result for set cover, a $ 4 / 3 $ inapproximability for min Steiner tree, and a $ 0.913 $ inapproximability for interval scheduling on two machines.", acknowledgement = ack-nhfb, articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chung:2011:CDK, author = "Kai-Min Chung and Omer Reingold and Salil Vadhan", title = "{S}-{T} connectivity on digraphs with a known stationary distribution", journal = j-TALG, volume = "7", number = "3", pages = "30:1--30:??", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978785", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a deterministic logspace algorithm for solving S-T Connectivity on directed graphs if: (i) we are given a stationary distribution of the random walk on the graph in which both of the input vertices $s$ and $t$ have nonnegligible probability mass and (ii) the random walk which starts at the source vertex $s$ has polynomial mixing time. This result generalizes the recent deterministic logspace algorithm for {$S$}--{$T$} Connectivity on undirected graphs [Reingold, 2008]. It identifies knowledge of the stationary distribution as the gap between the {$S$}--{$T$} Connectivity problems we know how to solve in logspace (L) and those that capture all of randomized logspace (RL).", acknowledgement = ack-nhfb, articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gairing:2011:RSF, author = "Martin Gairing and Burkhard Monien and Karsten Tiemann", title = "Routing (un-) splittable flow in games with player-specific affine latency functions", journal = j-TALG, volume = "7", number = "3", pages = "31:1--31:??", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978786", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this work we study weighted network congestion games with player-specific latency functions where selfish players wish to route their traffic through a shared network. We consider both the case of splittable and unsplittable traffic. Our main findings are as follows. For routing games on parallel links with linear latency functions, we introduce two new potential functions for unsplittable and for splittable traffic, respectively. We use these functions to derive results on the convergence to pure Nash equilibria and the computation of equilibria. For several generalizations of these routing games, we show that such potential functions do not exist. We prove tight upper and lower bounds on the price of anarchy for games with polynomial latency functions. All our results on the price of anarchy translate to general congestion games.", acknowledgement = ack-nhfb, articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Rosen:2011:RVB, author = "Adi Ros{\'e}n and Gabriel Scalosub", title = "Rate vs. buffer size --- greedy information gathering on the line", journal = j-TALG, volume = "7", number = "3", pages = "32:1--32:??", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978787", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider packet networks with limited buffer space at the nodes, and are interested in the question of maximizing the number of packets that arrive to destination rather than being dropped due to full buffers. We initiate a more refined analysis of the throughput competitive ratio of admission and scheduling policies in the Competitive Network Throughput model [Aiello et al. 2005], taking into account not only the network size but also the buffer size and the injection rate of the traffic. We specifically consider the problem of information gathering on the line, with limited buffer space, under adversarial traffic. We examine how the buffer size and the injection rate of the traffic affect the performance of the greedy protocol for this problem. We establish upper bounds on the competitive ratio of the greedy protocol in terms of the network size, the buffer size, and the adversary's rate, and present lower bounds which are tight up to constant factors. These results show, for example, that provisioning the network with sufficiently large buffers may substantially improve the performance of the greedy protocol in some cases, whereas for some high-rate adversaries, using larger buffers does not have any effect on the competitive ratio of the protocol.", acknowledgement = ack-nhfb, articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bonifaci:2011:MFT, author = "Vincenzo Bonifaci and Peter Korteweg and Alberto Marchetti-Spaccamela and Leen Stougie", title = "Minimizing flow time in the wireless gathering problem", journal = j-TALG, volume = "7", number = "3", pages = "33:1--33:??", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978788", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We address the problem of efficient data gathering in a wireless network through multihop communication. We focus on two objectives related to flow times, that is, the times spent by data packets in the system: minimization of the maximum flow time and minimization of the average flow time of the packets. For both problems we prove that, unless P = NP, no polynomial-time algorithm can approximate the optimal solution within a factor less than {$ \Omega (m^{1 - \epsilon }) $} for any {$ 0 < \epsilon < 1 $}, where {$m$} is the number of packets. We then assess the performance of two natural algorithms by proving that their cost remains within the optimal cost of the respective problem if we allow the algorithms to transmit data at a speed 5 times higher than that of the optimal solutions to which we compare them.", acknowledgement = ack-nhfb, articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Kranakis:2011:RRL, author = "Evangelos Kranakis and Danny Krizanc and Pat Morin", title = "Randomized rendezvous with limited memory", journal = j-TALG, volume = "7", number = "3", pages = "34:1--34:??", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978789", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a trade-off between the expected time for two identical agents to rendezvous on a synchronous, anonymous, oriented ring and the memory requirements of the agents. In particular, we show there exists a $ 2^t $ state agent which can achieve rendezvous on an $n$-node ring in expected time {$ O(n^2 / 2^t + 2^t) $} and that any {$ t / 2 $} state agent requires expected time {$ \Omega (n^2 / 2^t) $}. As a corollary we observe that {$ \Theta (\log \log n) $} bits of memory are necessary and sufficient to achieve rendezvous in linear time.", acknowledgement = ack-nhfb, articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Pemmaraju:2011:MCO, author = "Sriram V. Pemmaraju and Rajiv Raman and Kasturi Varadarajan", title = "Max-coloring and online coloring with bandwidths on interval graphs", journal = j-TALG, volume = "7", number = "3", pages = "35:1--35:??", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978790", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a graph $ G = (V, E) $ and positive integral vertex weights $ w \colon V \to N $, the max-coloring problem seeks to find a proper vertex coloring of $G$ whose color classes $ C_1, C_2, \ldots {}, C_k $, minimize $ \Sigma_i = 1^k \max_v \in C^i w(v) $. This problem, restricted to interval graphs, arises whenever there is a need to design dedicated memory managers that provide better performance than the general-purpose memory management of the operating system. Though this problem seems similar to the dynamic storage allocation problem, there are fundamental differences. We make a connection between max-coloring and online graph coloring and use this to devise a simple 2-approximation algorithm for max-coloring on interval graphs. We also show that a simple first-fit strategy, that is a natural choice for this problem, yields an 8-approximation algorithm. We show this result by proving that the first-fit algorithm for online coloring an interval graph $G$ uses no more than $ 8 c \chi (G) $ colors, significantly improving the bound of $ 26 c \chi (G) $ by Kierstead and Qin [1995]. We also show that the max-coloring problem is NP-hard. The problem of online coloring of intervals with bandwidths is a simultaneous generalization of online interval coloring and online bin packing. The input is a set $I$ of intervals, each interval $ i \in I $ having an associated bandwidth $ b(i) \in (0, 1] $. We seek an online algorithm that produces a coloring of the intervals such that for any color $c$ and any real $r$, the sum of the bandwidths of intervals containing $r$ and colored $c$ is at most $1$. Motivated by resource allocation problems, Adamy and Erlebach [2003] consider this problem and present an algorithm that uses at most 195 times the number of colors used by an optimal offline algorithm. Using the new analysis of first-fit coloring of interval graphs, we show that the Adamy-Erlebach algorithm is 35-competitive. Finally, we generalize the Adamy-Erlebach algorithm to a class of algorithms and show that a different instance from this class is 30-competitive.", acknowledgement = ack-nhfb, articleno = "35", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Khuller:2011:FFG, author = "Samir Khuller and Azarakhsh Malekian and Juli{\'a}n Mestre", title = "To fill or not to fill: {The} gas station problem", journal = j-TALG, volume = "7", number = "3", pages = "36:1--36:??", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978791", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article we study several routing problems that generalize shortest paths and the traveling salesman problem. We consider a more general model that incorporates the actual cost in terms of gas prices. We have a vehicle with a given tank capacity. We assume that at each vertex gas may be purchased at a certain price. The objective is to find the cheapest route to go from $s$ to $t$, or the cheapest tour visiting a given set of locations. We show that the problem of finding a cheapest plan to go from $s$ to $t$ can be solved in polynomial time. For most other versions, however, the problem is NP-complete and we develop polynomial-time approximation algorithms for these versions.", acknowledgement = ack-nhfb, articleno = "36", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Coppersmith:2011:OOG, author = "Don Coppersmith and Tomasz Nowicki and Giuseppe Paleologo and Charles Tresser and Chai Wah Wu", title = "The optimality of the online greedy algorithm in carpool and chairman assignment problems", journal = j-TALG, volume = "7", number = "3", pages = "37:1--37:??", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978792", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study several classes of related scheduling problems including the carpool problem, its generalization to arbitrary inputs and the chairman assignment problem. We derive both lower and upper bounds for online algorithms solving these problems. We show that the greedy algorithm is optimal among online algorithms for the chairman assignment problem and the generalized carpool problem. We also consider geometric versions of these problems and show how the bounds adapt to these cases.", acknowledgement = ack-nhfb, articleno = "37", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bille:2011:TIP, author = "Philip Bille and Inge Li Gortz", title = "The tree inclusion problem: {In} linear space and faster", journal = j-TALG, volume = "7", number = "3", pages = "38:1--38:47", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978793", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given two rooted, ordered, and labeled trees {$P$} and {$T$} the tree inclusion problem is to determine if {$P$} can be obtained from {$T$} by deleting nodes in {$T$}. This problem has recently been recognized as an important query primitive in XML databases. Kilpel{\"a}inen and Mannila [1995] presented the first polynomial-time algorithm using quadratic time and space. Since then several improved results have been obtained for special cases when {$P$} and {$T$} have a small number of leaves or small depth. However, in the worst case these algorithms still use quadratic time and space. Let {n$_S$}, {l$_S$}, and {d$_S$} denote the number of nodes, the number of leaves, and the depth of a tree {$ S \in P, T $}. In this article we show that the tree inclusion problem can be solved in space {$ O(n_T) $} and time: { $$ O(\min \left \{ l_P n_T, l_P n_T \log \log n_T + n_T, (n_P n_T) / (\log n_T) + n_T \log n_T \right \}) $$} This improves or matches the best known time complexities while using only linear space instead of quadratic. This is particularly important in practical applications, such as XML databases, where the space is likely to be a bottleneck.", acknowledgement = ack-nhfb, articleno = "38", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Laber:2011:IAH, author = "Eduardo Laber and Marco Molinaro", title = "Improved approximations for the hotlink assignment problem", journal = j-TALG, volume = "7", number = "3", pages = "39:1--39:??", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978794", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Let {$ G = (V, E) $} be a graph representing a Web site, where nodes correspond to pages and arcs to hyperlinks. In this context, hotlinks are defined as shortcuts (new arcs) added to Web pages of {$G$} in order to reduce the time spent by users to reach their desired information. In this article, we consider the problem where {$G$} is a rooted directed tree and the goal is minimizing the expected time spent by users by assigning at most {$k$} hotlinks to each node. For the most studied version of this problem where at most one hotlink can be added to each node, we prove the existence of two FPTAS's which optimize different objectives considered in the literature: one minimizes the expected user path length and the other maximizes the expected reduction in user path lengths. These results improve over a constant factor approximation for the expected length and over a PTAS for the expected reduction, both obtained recently in Jacobs [2007]. Indeed, these FPTAS's are essentially the best possible results one can achieve under the assumption that P {$ \neq $} NP. Another contribution we give here is a 16-approximation algorithm for the most general version of the problem where up to {$k$} hotlinks can be assigned from each node. This algorithm runs in {$ O(|V| \log |V|) $} time and it turns to be the first algorithm with constant approximation for this problem.", acknowledgement = ack-nhfb, articleno = "39", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Salvy:2011:PFF, author = "Bruno Salvy and Bob Sedgewick and Michele Soria and Wojciech Szpankowski and Brigitte Vallee", title = "{Philippe Flajolet}, the father of analytic combinatorics", journal = j-TALG, volume = "7", number = "4", pages = "40:1--40:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000808", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "40", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Dvorak:2011:TCT, author = "Zdenek Dvor{\'a}k and Ken-Ichi Kawarabayashi and Robin Thomas", title = "Three-coloring triangle-free planar graphs in linear time", journal = j-TALG, volume = "7", number = "4", pages = "41:1--41:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000809", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Gr{\"o}tzsch's theorem states that every triangle-free planar graph is 3-colorable, and several relatively simple proofs of this fact were provided by Thomassen and other authors. It is easy to convert these proofs into quadratic-time algorithms to find a 3-coloring, but it is not clear how to find such a coloring in linear time (Kowalik used a nontrivial data structure to construct an {$ O(n \log n) $} algorithm). We design a linear-time algorithm to find a 3-coloring of a given triangle-free planar graph. The algorithm avoids using any complex data structures, which makes it easy to implement. As a by-product, we give a yet simpler proof of Gr{\"o}tzsch's theorem.", acknowledgement = ack-nhfb, articleno = "41", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Moran:2011:PCR, author = "Shlomo Moran and Sagi Snir and Wing-Kin Sung", title = "Partial convex recolorings of trees and galled networks: {Tight} upper and lower bounds", journal = j-TALG, volume = "7", number = "4", pages = "42:1--42:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000810", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A coloring of a graph is convex if the vertices that pertain to any color induce a connected subgraph; a partial coloring (which assigns colors to a subset of the vertices) is convex if it can be completed to a convex (total) coloring. Convex coloring has applications in fields such as phylogenetics, communication or transportation networks, etc. When a coloring of a graph is not convex, a natural question is how far it is from a convex one. This problem is denoted as convex recoloring (CR). While the initial works on CR defined and studied the problem on trees, recent efforts aim at either generalizing the underlying graphs or specializing the input colorings. In this work, we extend the underlying graph and the input coloring to partially colored galled networks. We show that although determining whether a coloring is convex on an arbitrary network is hard, it can be found efficiently on galled networks. We present a fixed parameter tractable algorithm that finds the recoloring distance of such a network whose running time is quadratic in the network size and exponential in that distance. This complexity is achieved by amortized analysis that uses a novel technique for contracting colored graphs that seems to be of independent interest.", acknowledgement = ack-nhfb, articleno = "42", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cabello:2011:GCF, author = "Sergio Cabello and Panos Giannopoulos and Christian Knauer and D{\'a}niel Marx and G{\"u}nter Rote", title = "Geometric clustering: {Fixed-parameter} tractability and lower bounds with respect to the dimension", journal = j-TALG, volume = "7", number = "4", pages = "43:1--43:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000811", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the parameterized complexity of the $k$-center problem on a given $n$-point set {$P$} in {$ R^d $}, with the dimension {$d$} as the parameter. We show that the rectilinear 3-center problem is fixed-parameter tractable, by giving an algorithm that runs in {$ O(n \log n) $} time for any fixed dimension d. On the other hand, we show that this is unlikely to be the case with both the Euclidean and rectilinear {$k$}-center problems for any {$ k \geq 2 $} and {$ k \geq 4 $} respectively. In particular, we prove that deciding whether {$P$} can be covered by the union of 2 balls of given radius or by the union of 4 cubes of given side length is W[1]-hard with respect to {$d$}, and thus not fixed-parameter tractable unless FPT = W[1]. For the Euclidean case, we also show that even an {$ n^{o(d)} $}-time algorithm does not exist, unless there is a {2$^{o(n)}$}-time algorithm for $n$-variable 3SAT, that is, the Exponential Time Hypothesis fails.", acknowledgement = ack-nhfb, articleno = "43", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bonsma:2011:TBF, author = "Paul Bonsma and Frederic Dorn", title = "Tight bounds and a fast {FPT} algorithm for directed {Max-Leaf Spanning Tree}", journal = j-TALG, volume = "7", number = "4", pages = "44:1--44:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000812", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "An out-tree {$T$} of a directed graph {$D$} is a rooted tree subgraph with all arcs directed outwards from the root. An out-branching is a spanning out-tree. By {$ l(D) $} and {$ l_s(D) $}, we denote the maximum number of leaves over all out-trees and out-branchings of {$D$}, respectively. We give fixed parameter tractable algorithms for deciding whether {$ l_s(D) \geq k $} and whether {$ l(D) \geq k $} for a digraph {$D$} on {$n$} vertices, both with time complexity {$ 2^{o(k \log k)} \cdot n^{o(1)} $}. This answers an open question whether the problem for out-branchings is in FPT, and improves on the previous complexity of {$ 2^{o(k \log 2 k)} \cdot n^{o(1)} $} in the case of out-trees. To obtain the complexity bound in the case of out-branchings, we prove that when all arcs of {$D$} are part of at least one out-branching, {$ l_s(D) \geq l(D) / 3 $}. The second bound we prove in this article states that for strongly connected digraphs {$D$} with minimum in-degree {$ 3, l_s(D) \geq \Theta (\sqrt n) $}, where previously {$ l_s(D) \geq \Theta (3 \sqrt n) $} was the best known bound. This bound is tight, and also holds for the larger class of digraphs with minimum in-degree {$3$} in which every arc is part of at least one out-branching.", acknowledgement = ack-nhfb, articleno = "44", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Roditty:2011:APS, author = "Liam Roditty and Asaf Shapira", title = "All-pairs shortest paths with a sublinear additive error", journal = j-TALG, volume = "7", number = "4", pages = "45:1--45:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000813", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show that, for every $ 0 \leq p \leq 1 $, there is an {$ O(n^{2.575 - p / (7.4 - 2.3 p)}) $}-time algorithm that given a directed graph with small positive integer weights, estimates the length of the shortest path between every pair of vertices {$ u, v $} in the graph to within an additive error {$ \delta^p(u, v) $}, where {$ \delta (u, v) $} is the exact length of the shortest path between $u$ and $v$. This algorithm runs faster than the fastest algorithm for computing exact shortest paths for any $ 0 < p \leq 1 $. Previously the only way to ``beat'' the running time of the exact shortest path algorithms was by applying an algorithm of Zwick [2002] that approximates the shortest path distances within a multiplicative error of $ (1 + \epsilon) $. Our algorithm thus gives a smooth qualitative and quantitative transition between the fastest exact shortest paths algorithm, and the fastest approximation algorithm with a linear additive error. In fact, the main ingredient we need in order to obtain the above result, which is also interesting in its own right, is an algorithm for computing $ (1 + \epsilon) $ multiplicative approximations for the shortest paths, whose running time is faster than the running time of Zwick's approximation algorithm when $ \epsilon \ll 1 $ and the graph has small integer weights.", acknowledgement = ack-nhfb, articleno = "45", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Pritchard:2011:FCS, author = "David Pritchard and Ramakrishna Thurimella", title = "Fast computation of small cuts via cycle space sampling", journal = j-TALG, volume = "7", number = "4", pages = "46:1--46:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000814", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We describe a new sampling-based method to determine cuts in an undirected graph. For a graph {$ (V, E) $}, its cycle space is the family of all subsets of {$E$} that have even degree at each vertex. We prove that with high probability, sampling the cycle space identifies the cuts of a graph. This leads to simple new linear-time sequential algorithms for finding all cut edges and cut pairs (a set of 2 edges that form a cut) of a graph. In the model of distributed computing in a graph {$ G = (V, E) $} with {$ O(\log |V|) $}-bit messages, our approach yields faster algorithms for several problems. The diameter of {$G$} is denoted by {$D$}, and the maximum degree by {$ \Delta $}. We obtain simple {$ O(D) $}-time distributed algorithms to find all cut edges, 2-edge-connected components, and cut pairs, matching or improving upon previous time bounds. Under natural conditions these new algorithms are universally optimal-that is, a {$ \Omega (D) $}-time lower bound holds on every graph. We obtain a {$ O(D + \Delta / \log |V|) $}-time distributed algorithm for finding cut vertices; this is faster than the best previous algorithm when {$ \Delta, D = O(\sqrt |V|) $}. A simple extension of our work yields the first distributed algorithm with sub-linear time for 3-edge-connected components. The basic distributed algorithms are Monte Carlo, but they can be made Las Vegas without increasing the asymptotic complexity. In the model of parallel computing on the EREW PRAM, our approach yields a simple algorithm with optimal time complexity {$ O(\log V) $} for finding cut pairs and 3-edge-connected components.", acknowledgement = ack-nhfb, articleno = "46", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chang:2011:BSA, author = "Jessica Chang and Thomas Erlebach and Renars Gailis and Samir Khuller", title = "Broadcast scheduling: {Algorithms} and complexity", journal = j-TALG, volume = "7", number = "4", pages = "47:1--47:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000815", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Broadcast Scheduling is a popular method for disseminating information in response to client requests. There are $n$ pages of information, and clients request pages at different times. However, multiple clients can have their requests satisfied by a single broadcast of the requested page. In this article, we consider several related broadcast scheduling problems. One central problem we study simply asks to minimize the maximum response time (over all requests). Another related problem we consider is the version in which every request has a release time and a deadline, and the goal is to maximize the number of requests that meet their deadlines. While approximation algorithms for both these problems were proposed several years back, it was not known if they were NP-complete. One of our main results is that both these problems are NP-complete. In addition, we use the same unified approach to give a simple NP-completeness proof for minimizing the sum of response times. A very complicated proof was known for this version. Furthermore, we give a proof that FIFO is a 2-competitive online algorithm for minimizing the maximum response time (this result had been claimed earlier with no proof) and that there is no better deterministic online algorithm (this result was claimed earlier as well, but with an incorrect proof).", acknowledgement = ack-nhfb, articleno = "47", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Calinescu:2011:IAA, author = "Gruia Calinescu and Amit Chakrabarti and Howard Karloff and Yuval Rabani", title = "An improved approximation algorithm for resource allocation", journal = j-TALG, volume = "7", number = "4", pages = "48:1--48:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000816", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the problem of finding a most profitable subset of $n$ given tasks, each with a given start and finish time as well as profit and resource requirement, that at no time exceeds the quantity {$B$} of available resource. We show that this NP-hard Resource Allocation problem can be {$ (1 / 2 - \epsilon) $}-approximated in randomized polynomial time, which improves upon earlier approximation results.", acknowledgement = ack-nhfb, articleno = "48", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Fotakis:2011:MFL, author = "Dimitris Fotakis", title = "Memoryless facility location in one pass", journal = j-TALG, volume = "7", number = "4", pages = "49:1--49:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000817", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present the first one-pass memoryless algorithm for metric Facility Location that maintains a set of facilities approximating the optimal facility configuration within a constant factor. The algorithm is randomized and very simple to state and implement. It processes the demand points one-by-one as they arrive, and keeps in memory only the facility locations currently open. We prove that its competitive ratio is less than 14 in the special case of uniform facility costs, and less than 49 in the general case of nonuniform facility costs.", acknowledgement = ack-nhfb, articleno = "49", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Han:2011:NUB, author = "Xin Han and Francis Y. L. Chin and Hing-Fung Ting and Guochuan Zhang and Yong Zhang", title = "A new upper bound $ 2.5545 $ on {$2$D} {Online Bin Packing}", journal = j-TALG, volume = "7", number = "4", pages = "50:1--50:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000818", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The 2D Online Bin Packing is a fundamental problem in Computer Science and the determination of its asymptotic competitive ratio has research attention. In a long series of papers, the lower bound of this ratio has been improved from 1.808, 1.856 to 1.907 and its upper bound reduced from 3.25, 3.0625, 2.8596, 2.7834 to 2.66013. In this article, we rewrite the upper bound record to 2.5545. Our idea for the improvement is as follows. In 2002, Seiden and van Stee [Seiden and van Stee 2003] proposed an elegant algorithm called {$ H \otimes C $}, comprised of the Harmonic algorithm {$H$} and the Improved Harmonic algorithm {$C$}, for the two-dimensional online bin packing problem and proved that the algorithm has an asymptotic competitive ratio of at most 2.66013. Since the best known online algorithm for one-dimensional bin packing is the Super Harmonic algorithm [Seiden 2002], a natural question to ask is: could a better upper bound be achieved by using the Super Harmonic algorithm instead of the Improved Harmonic algorithm? However, as mentioned in Seiden and van Stee [2003], the previous analysis framework does not work. In this article, we give a positive answer for this question. A new upper bound of 2.5545 is obtained for 2-dimensional online bin packing. The main idea is to develop new weighting functions for the Super Harmonic algorithm and propose new techniques to bound the total weight in a rectangular bin.", acknowledgement = ack-nhfb, articleno = "50", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Edmonds:2011:CCR, author = "Jeff Edmonds and Kirk Pruhs", title = "Cake cutting really is not a piece of cake", journal = j-TALG, volume = "7", number = "4", pages = "51:1--51:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000819", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the well-known cake cutting problem in which a protocol wants to divide a cake among $ n \geq 2 $ players in such a way that each player believes that they got a fair share. The standard Robertson-Webb model allows the protocol to make two types of queries, Evaluation and Cut, to the players. A deterministic divide-and-conquer protocol with complexity {$ O(n \log n) $} is known. We provide the first a {$ \Omega (n \log n) $} lower bound on the complexity of any deterministic protocol in the standard model. This improves previous lower bounds, in that the protocol is allowed to assign to a player a piece that is a union of intervals and only guarantee approximate fairness. We accomplish this by lower bounding the complexity to find, for a single player, a piece of cake that is both rich in value, and thin in width. We then introduce a version of cake cutting in which the players are able to cut with only finite precision. In this case, we can extend the {$ \Omega (n \log n) $} lower bound to include randomized protocols.", acknowledgement = ack-nhfb, articleno = "51", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Barbay:2011:SIS, author = "J{\'e}r{\'e}my Barbay and Meng He and J. Ian Munro and Srinivasa Rao Satti", title = "Succinct indexes for strings, binary relations and multilabeled trees", journal = j-TALG, volume = "7", number = "4", pages = "52:1--52:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000820", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We define and design succinct indexes for several abstract data types (ADTs). The concept is to design auxiliary data structures that ideally occupy asymptotically less space than the information-theoretic lower bound on the space required to encode the given data, and support an extended set of operations using the basic operators defined in the ADT. The main advantage of succinct indexes as opposed to succinct (integrated data/index) encodings is that we make assumptions only on the ADT through which the main data is accessed, rather than the way in which the data is encoded. This allows more freedom in the encoding of the main data. In this article, we present succinct indexes for various data types, namely strings, binary relations and multilabeled trees. Given the support for the interface of the ADTs of these data types, we can support various useful operations efficiently by constructing succinct indexes for them. When the operators in the ADTs are supported in constant time, our results are comparable to previous results, while allowing more flexibility in the encoding of the given data. Using our techniques, we design a succinct encoding that represents a string of length $n$ over an alphabet of size $ \sigma $ using {$ n H_k (S) + \lg \sigma \cdot o(n) + O(n \lg \sigma / \lg \lg \lg \sigma) $} bits to support access\slash rank\slash select operations in {$ o((\lg \lg \sigma)^{1 + \epsilon }) $} time, for any fixed constant {$ \epsilon > 0 $}. We also design a succinct text index using {$ n H_0 (S) + O(n \lg \sigma / \lg \lg \sigma) $} bits that supports finding all the occ occurrences of a given pattern of length {$m$} in {$ O(m \lg \lg \sigma + {\rm occ} \lg n / \lg^\epsilon \sigma) $} time, for any fixed constant {$ 0 < \epsilon < 1 $}. Previous results on these two problems either have a {$ \lg \sigma $} factor instead of {$ \lg \lg \sigma $} in the running time, or are not compressed. Finally, we present succinct encodings of binary relations and multi-labeled trees that are more compact than previous structures.", acknowledgement = ack-nhfb, articleno = "52", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Russo:2011:FCS, author = "Lu{\'\i}s M. S. Russo and Gonzalo Navarro and Arlindo L. Oliveira", title = "{Fully} compressed suffix trees", journal = j-TALG, volume = "7", number = "4", pages = "53:1--53:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000821", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Suffix trees are by far the most important data structure in stringology, with a myriad of applications in fields like bioinformatics and information retrieval. Classical representations of suffix trees require {$ \Theta (n \log n) $} bits of space, for a string of size {$n$}. This is considerably more than the {$ n \log_2 \sigma $} bits needed for the string itself, where {$ \sigma $} is the alphabet size. The size of suffix trees has been a barrier to their wider adoption in practice. Recent compressed suffix tree representations require just the space of the compressed string plus {$ \Theta (n) $} extra bits. This is already spectacular, but the linear extra bits are still unsatisfactory when {$ \sigma $} is small as in DNA sequences. In this article, we introduce the first compressed suffix tree representation that breaks this {$ \Theta (n) $}-bit space barrier. The Fully Compressed Suffix Tree (FCST) representation requires only sublinear space on top of the compressed text size, and supports a wide set of navigational operations in almost logarithmic time. This includes extracting arbitrary text substrings, so the FCST replaces the text using almost the same space as the compressed text. An essential ingredient of FCSTs is the lowest common ancestor (LCA) operation. We reveal important connections between LCAs and suffix tree navigation. We also describe how to make FCSTs dynamic, that is, support updates to the text. The dynamic FCST also supports several operations. In particular, it can build the static FCST within optimal space and polylogarithmic time per symbol. Our theoretical results are also validated experimentally, showing that FCSTs are very effective in practice as well.", acknowledgement = ack-nhfb, articleno = "53", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Izsak:2011:CPM, author = "Alexander Izsak and Nicholas Pippenger", title = "Carry propagation in multiplication by constants", journal = j-TALG, volume = "7", number = "4", pages = "54:1--54:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000822", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Suppose that a random $n$-bit number V is multiplied by an odd constant {$ M \geq 3 $}, by adding shifted versions of the number {$V$} corresponding to the {$1$} s in the binary representation of the constant {$M$}. Suppose further that the additions are performed by carry-save adders until the number of summands is reduced to two, at which time the final addition is performed by a carry-propagate adder. We show that in this situation the distribution of the length of the longest carry-propagation chain in the final addition is the same (up to terms tending to {$0$} as {$ n \to \infty $}) as when two independent {$n$}-bit numbers are added, and in particular the mean and variance are the same (again up to terms tending to 0). This result applies to all possible orders of performing the carry-save additions.", acknowledgement = ack-nhfb, articleno = "54", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Guha:2012:AUR, author = "Sudipto Guha and Kamesh Munagala", title = "Adaptive Uncertainty Resolution in {Bayesian} Combinatorial Optimization Problems", journal = j-TALG, volume = "8", number = "1", pages = "1:1--1:??", month = jan, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2071379.2071380", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Mar 16 15:33:03 MDT 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In several applications such as databases, planning, and sensor networks, parameters such as selectivity, load, or sensed values are known only with some associated uncertainty. The performance of such a system (as captured by some objective function over the parameters) is significantly improved if some of these parameters can be probed or observed. In a resource constrained situation, deciding which parameters to observe in order to optimize system performance, itself becomes an interesting and important optimization problem. This general problem is the focus of this article. One of the most important considerations in this framework is whether adaptivity is required for the observations. Adaptive observations introduce blocking or sequential operations in the system whereas nonadaptive observations can be performed in parallel. One of the important questions in this regard is to characterize the benefit of adaptivity for probes and observation. We present general techniques for designing constant factor approximations to the optimal observation schemes for several widely used scheduling and metric objective functions. We show a unifying technique that relates this optimization problem to the outlier version of the corresponding deterministic optimization. By making this connection, our technique shows constant factor upper bounds for the benefit of adaptivity of the observation schemes. We show that while probing yields significant improvement in the objective function, being adaptive about the probing is not beneficial beyond constant factors.", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Mahdian:2012:OOU, author = "Mohammad Mahdian and Hamid Nazerzadeh and Amin Saberi", title = "Online {Optimization} with {Uncertain Information}", journal = j-TALG, volume = "8", number = "1", pages = "2:1--2:??", month = jan, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2071379.2071381", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Mar 16 15:33:03 MDT 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce a new framework for designing online algorithms that can incorporate additional information about the input sequence, while maintaining a reasonable competitive ratio if the additional information is incorrect. Within this framework, we present online algorithms for several problems including allocation of online advertisement space, load balancing, and facility location.", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Haeupler:2012:ICD, author = "Bernhard Haeupler and Telikepalli Kavitha and Rogers Mathew and Siddhartha Sen and Robert E. Tarjan", title = "Incremental {Cycle Detection}, {Topological Ordering}, and {Strong Component Maintenance}", journal = j-TALG, volume = "8", number = "1", pages = "3:1--3:??", month = jan, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2071379.2071382", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Mar 16 15:33:03 MDT 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present two online algorithms for maintaining a topological order of a directed $n$-vertex acyclic graph as arcs are added, and detecting a cycle when one is created. Our first algorithm handles $m$ arc additions in {$ O(m^{3 / 2}) $} time. For sparse graphs {$ (m / n = O(1)) $}, this bound improves the best previous bound by a logarithmic factor, and is tight to within a constant factor among algorithms satisfying a natural locality property. Our second algorithm handles an arbitrary sequence of arc additions in {$ O(n^{5 / 2}) $} time. For sufficiently dense graphs, this bound improves the best previous bound by a polynomial factor. Our bound may be far from tight: we show that the algorithm can take {$ \Omega (n^2 2^{\sqrt {2 \lg n}}) $} time by relating its performance to a generalization of the {$k$}-levels problem of combinatorial geometry. A completely different algorithm running in {$ \Theta (n^2 \log n) $} time was given recently by Bender, Fineman, and Gilbert. We extend both of our algorithms to the maintenance of strong components, without affecting the asymptotic time bounds.", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Frigo:2012:COA, author = "Matteo Frigo and Charles E. Leiserson and Harald Prokop and Sridhar Ramachandran", title = "Cache-Oblivious Algorithms", journal = j-TALG, volume = "8", number = "1", pages = "4:1--4:??", month = jan, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2071379.2071383", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Mar 16 15:33:03 MDT 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article presents asymptotically optimal algorithms for rectangular matrix transpose, fast Fourier transform (FFT), and sorting on computers with multiple levels of caching. Unlike previous optimal algorithms, these algorithms are cache oblivious: no variables dependent on hardware parameters, such as cache size and cache-line length, need to be tuned to achieve optimality. Nevertheless, these algorithms use an optimal amount of work and move data optimally among multiple levels of cache. For a cache with size {$M$} and cache-line length {$B$} where {$ M = \Omega (B^2) $}, the number of cache misses for an {$ m \times n $} matrix transpose is {$ \Theta (1 + m n / B) $}. The number of cache misses for either an {$n$}-point FFT or the sorting of {$n$} numbers is {$ \Theta (1 + (n / B)(1 + \log M n)) $}. We also give a {$ \Theta (m n p) $}-work algorithm to multiply an {$ m \times n $} matrix by an {$ n \times p $} matrix that incurs {$ \Theta (1 + (m n + n p + m p) / B + m n p / B \sqrt {M}) $} cache faults. We introduce an `ideal-cache' model to analyze our algorithms. We prove that an optimal cache-oblivious algorithm designed for two levels of memory is also optimal for multiple levels and that the assumption of optimal replacement in the ideal-cache model can be simulated efficiently by LRU replacement. We offer empirical evidence that cache-oblivious algorithms perform well in practice.", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chlebus:2012:AQM, author = "Bogdan S. Chlebus and Dariusz R. Kowalski and Mariusz A. Rokicki", title = "Adversarial Queuing on the Multiple Access Channel", journal = j-TALG, volume = "8", number = "1", pages = "5:1--5:??", month = jan, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2071379.2071384", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Mar 16 15:33:03 MDT 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study deterministic broadcasting on multiple access channels when packets are injected continuously. The quality of service is considered in the framework of adversarial queuing. An adversary is determined by injection rate and burstiness, the latter denoting the number of packets that can be injected simultaneously in a round. We consider only injection rates that are less than $1$. A protocol is stable when the numbers of packets in queues stay bounded at all rounds, and it is of fair latency when waiting times of packets in queues are {$ O({\rm burstiness} / {\rm rate}) $}. For channels with collision detection, we give a full-sensing protocol of fair latency for injection rates that are at most {$ 1 \over 2 (\lceil \lg n \rceil + 1) $}, where {$n$} is the number of stations, and show that fair latency is impossible to achieve for injection rates that are {$ \omega (1 \over \log n) $}. For channels without collision detection, we present a full-sensing protocol of fair latency for injection rates that are at most $ 1 \over c \lg^2 n $, for some $ c > 0 $. We show that there exists an acknowledgment-based protocol that has fair latency for injection rates that are at most $ 1 \over c n \lg^2 n $, for some $ c > 0 $, and develop an explicit acknowledgment-based protocol of fair latency for injection rates that are at most $ 1 \over 27 n^2 \ln n $. Regarding impossibility to achieve just stability by restricted protocols, we prove that no acknowledgment-based protocol can be stable for injection rates larger than $ 3 \over 1 + \lg n $.", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chen:2012:IEC, author = "Jianer Chen and Yang Liu and Songjian Lu and Sing-Hoi Sze and Fenghui Zhang", title = "Iterative Expansion and Color Coding: An Improved Algorithm for {$3$D}-Matching", journal = j-TALG, volume = "8", number = "1", pages = "6:1--6:??", month = jan, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2071379.2071385", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Mar 16 15:33:03 MDT 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The research in the parameterized 3d-matching problem has yielded a number of new algorithmic techniques and an impressive list of improved algorithms. In this article, a new deterministic algorithm for the problem is developed that integrates and improves a number of known techniques, including greedy localization, dynamic programming, and color coding. The new algorithm, which either constructs a matching of $k$ triples in a given triple set or correctly reports that no such a matching exists, runs in time {$ O*(2.80^3 k) $}, improving a long list of previous algorithms for the problem.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bocker:2012:IFP, author = "Sebastian B{\"o}cker and Quang Bao Anh Bui and Anke Truss", title = "Improved Fixed-Parameter Algorithms for Minimum-Flip Consensus Trees", journal = j-TALG, volume = "8", number = "1", pages = "7:1--7:??", month = jan, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2071379.2071386", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Mar 16 15:33:03 MDT 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In computational phylogenetics, the problem of constructing a consensus tree for a given set of rooted input trees has frequently been addressed. In this article we study the Minimum-Flip Problem: the input trees are transformed into a binary matrix, and we want to find a perfect phylogeny for this matrix using a minimum number of flips, that is, corrections of single entries in the matrix. The graph-theoretical formulation of the problem is as follows: Given a bipartite graph {$ G = (V t \cup V c, E) $}, the task is to find a minimum set of edge modifications such that the resulting graph has no induced path with four edges that starts and ends in Vt, where Vt corresponds to the taxa set and Vc corresponds to the character set. We present two fixed-parameter algorithms for the Minimum-Flip Problem, one with running time {$ O(4.83 k + \poly (m, n)) $} and another one with running time {$ O(4.42 k + \poly (m, n)) $} for {$n$} taxa, {$m$} characters, {$k$} flips, and $ \poly (m, n) $ denotes a polynomial function in $m$ and $n$. Additionally, we discuss several heuristic improvements. We also report computational results on phylogenetic data.", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cygan:2012:EFE, author = "Marek Cygan and Marcin Pilipczuk", title = "Even Faster Exact Bandwidth", journal = j-TALG, volume = "8", number = "1", pages = "8:1--8:??", month = jan, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2071379.2071387", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Mar 16 15:33:03 MDT 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We deal with exact algorithms for Bandwidth, a long studied NP-hard problem. For a long time nothing better than the trivial {$ O^\ast (n!)^1 $} exhaustive search was known. In 2000, Feige and Kilian [Feige 2000] came up with a {$ O^\ast (10 n) $}-time and polynomial space algorithm. In this article we present a new algorithm that solves Bandwidth in {$ O^\ast (5 n) $} time and {$ O^\ast (2 n) $} space. Then, we take a closer look and introduce a major modification that makes it run in {$ O(4.83 n) $} time with a cost of a {$ O^\ast (4 n) $} space complexity. This modification allowed us to perform the Measure \& Conquer analysis for the time complexity which was not used for graph layout problems before.", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Aumann:2012:DIG, author = "Yonatan Aumann and Moshe Lewenstein and Oren Melamud and Ron Pinter and Zohar Yakhini", title = "Dotted interval graphs", journal = j-TALG, volume = "8", number = "2", pages = "9:1--9:??", month = apr, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2151171.2151172", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:57 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce a generalization of interval graphs, which we call Dotted Interval Graphs (DIG). A dotted interval graph is an intersection graph of arithmetic progressions (dotted intervals). Coloring of dotted interval graphs naturally arises in the context of high throughput genotyping. We study the properties of dotted interval graphs, with a focus on coloring. We show that any graph is a DIG, but that DIG$_d$ graphs, that is, DIGs in which the arithmetic progressions have a jump of at most $d$, form a strict hierarchy. We show that coloring DIG$_d$ graphs is NP-complete even for $ d = 2 $. For any fixed $d$, we provide a $ 5 / 6 d + o(d) $ approximation for the coloring of DIG$_d$ graphs. Finally, we show that finding the maximal clique in DIG$_d$ graphs is fixed parameter tractable in $d$.", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bose:2012:SGI, author = "Prosenjit Bose and Eric Y. Chen and Meng He and Anil Maheshwari and Pat Morin", title = "Succinct geometric indexes supporting point location queries", journal = j-TALG, volume = "8", number = "2", pages = "10:1--10:??", month = apr, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2151171.2151173", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:57 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We propose designing data structures called succinct geometric indexes of negligible space (more precisely, $ o(n) $ bits) that support geometric queries in optimal time, by taking advantage of the $n$ points in the dataset permuted and stored elsewhere as a sequence. Our first and main result is a succinct geometric index that can answer point location queries, a fundamental problem in computational geometry, on planar triangulations in {$ O(\lg n) $} time. We also design three variants of this index. The first supports point location using {$ \lg n + 2 \sqrt {\lg n} + O(\lg^{1 / 4} n) $} point-line comparisons. The second supports point location in {$ o(\lg n) $} time when the coordinates are integers bounded by {$U$}. The last variant can answer point location queries in {$ O(H + 1) $} expected time, where {$H$} is the entropy of the query distribution. These results match the query efficiency of previous point location structures that occupy {$ O(n) $} words or {$ O(n \lg n) $} bits, while saving drastic amounts of space. We generalize our succinct geometric index to planar subdivisions, and design indexes for other types of queries. Finally, we apply our techniques to design the first implicit data structures that support point location in {$ O(\lg^2 n) $} time.", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Drmota:2012:PAC, author = "Michael Drmota and Reinhard Kutzelnigg", title = "A precise analysis of {Cuckoo} hashing", journal = j-TALG, volume = "8", number = "2", pages = "11:1--11:36", month = apr, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2151171.2151174", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:57 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/hash.bib; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Cuckoo hashing was introduced by Pagh and Rodler in 2001. Its main feature is that it provides constant worst-case search time. The aim of this article is to present a precise average case analysis of Cuckoo hashing. In particular, we determine the probability that Cuckoo hashing produces no conflicts and give an upper bound for the construction time, that is linear in the size of the table. The analysis rests on a generating function approach to the so called Cuckoo Graph, a random bipartite graph, and an application of a double saddle point method to obtain asymptotic expansions. Furthermore, we provide some results concerning the structure of these kinds of random graphs. Our results extend the analysis of Devroye and Morin [2003]. Additionally, we provide numerical results confirming the mathematical analysis.", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Yi:2012:MOT, author = "Ke Yi and Qin Zhang", title = "Multidimensional online tracking", journal = j-TALG, volume = "8", number = "2", pages = "12:1--12:??", month = apr, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2151171.2151175", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:57 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We propose and study a new class of online problems, which we call online tracking. Suppose an observer, say Alice, observes a multivalued function {$ f : Z^+ \to Z^d $} over time in an online fashion, that is, she only sees {$ f(t) $} for {$ t \leq t_{\rm now} $} where {$ t_{\rm now} $} is the current time. She would like to keep a tracker, say Bob, informed of the current value of $f$ at all times. Under this setting, Alice could send new values of $f$ to Bob from time to time, so that the current value of $f$ is always within a distance of {$ \Delta $} to the last value received by Bob. We give competitive online algorithms whose communication costs are compared with the optimal offline algorithm that knows the entire {$f$} in advance. We also consider variations of the problem where Alice is allowed to send predictions to Bob, to further reduce communication for well-behaved functions. These online tracking problems have a variety of application, ranging from sensor monitoring, location-based services, to publish/subscribe systems.", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Demaine:2012:PAN, author = "Erik D. Demaine and Mohammadtaghi Hajiaghayi and Hamid Mahini and Morteza Zadimoghaddam", title = "The price of anarchy in network creation games", journal = j-TALG, volume = "8", number = "2", pages = "13:1--13:??", month = apr, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2151171.2151176", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:57 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study Nash equilibria in the setting of network creation games introduced recently by Fabrikant, Luthra, Maneva, Papadimitriou, and Shenker. In this game we have a set of selfish node players, each creating some incident links, and the goal is to minimize $ \alpha $ times the cost of the created links plus sum of the distances to all other players. Fabrikant et al. proved an upper bound {$ O(\sqrt \alpha) $} on the price of anarchy: the relative cost of the lack of coordination. Albers, Eilts, Even-Dar, Mansour, and Roditty show that the price of anarchy is constant for {$ \alpha = O(\sqrt n) $} and for {$ \alpha \geq 12 n \lceil \lg n \rceil $}, and that the price of anarchy is {$ 15 (1 + (\min {\alpha^2 / n, n^2 / \alpha })^{1 / 3}) $} for any {$ \alpha $}. The latter bound shows the first sublinear worst-case bound, {$ O(n^{1 / 3}) $}, for all {$ \alpha $}. But no better bound is known for {$ \alpha $} between {$ \omega (\sqrt n) $} and $ o(n \lg n) $. Yet $ \alpha \approx n $ is perhaps the most interesting range, for it corresponds to considering the average distance (instead of the sum of distances) to other nodes to be roughly on par with link creation (effectively dividing $ \alpha $ by $n$). In this article, we prove the first $ o(n^\epsilon) $ upper bound for general $ \alpha $, namely {$ 2^{O(\sqrt {\lg n})} $}. We also prove a constant upper bound for {$ \alpha = O({n^{1 \epsilon }}) $} for any fixed {$ \epsilon > 0 $}, substantially reducing the range of {$ \alpha $} for which constant bounds have not been obtained. Along the way, we also improve the constant upper bound by Albers et al. (with the lead constant of {$ 15 $}) to $6$ for $ \alpha < (n / 2)^{1 / 2} $ and to $4$ for $ \alpha < (n / 2)^{1 / 3} $. Next we consider the bilateral network variant of Corbo and Parkes, in which links can be created only with the consent of both endpoints and the link price is shared equally by the two. Corbo and Parkes show an upper bound of {$ O(\sqrt \alpha) $} and a lower bound of {$ \Omega (\lg \alpha) $} for {$ \alpha \leq n $}. In this article, we show that in fact the upper bound {$ O(\sqrt \alpha) $} is tight for {$ \alpha \leq n $}, by proving a matching lower bound of {$ \Omega (\sqrt \alpha) $}. For {$ \alpha > n $}, we prove that the price of anarchy is {$ \Theta (n / \sqrt \alpha) $}. Finally we introduce a variant of both network creation games, in which each player desires to minimize {$ \alpha $} times the cost of its created links plus the maximum distance (instead of the sum of distances) to the other players. This variant of the problem is naturally motivated by considering the worst case instead of the average case. Interestingly, for the original (unilateral) game, we show that the price of anarchy is at most {$2$} for {$ \alpha \geq n $}, {$ O(\min \{ 4^{\sqrt {\lg n}}, (n / \alpha)^{1 / 3} \}) $} for {$ 2 \sqrt {\lg n} \leq \alpha \leq n $}, and {$ O(n^{2 / \alpha }) $} for {$ \alpha < 2 \sqrt {\lg n} $}. For the bilateral game, we prove matching upper and lower bounds of {$ \Theta (n / \alpha + 1) $} for {$ \alpha \leq n $}, and an upper bound of {$2$} for {$ \alpha > n $}.", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ye:2012:EG, author = "Yuli Ye and Allan Borodin", title = "Elimination graphs", journal = j-TALG, volume = "8", number = "2", pages = "14:1--14:??", month = apr, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2151171.2151177", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:57 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article we study graphs with inductive neighborhood properties. Let {$P$} be a graph property, a graph {$ G = (V, E) $} with {$n$} vertices is said to have an inductive neighborhood property with respect to {$P$} if there is an ordering of vertices {$ v_1 $}, \ldots, {$ v_n $} such that the property {$P$} holds on the induced subgraph {$ G[N(v_i) \cap V_i] $}, where {$ N(v_i) $} is the neighborhood of {$ v_i $} and {$ V_i = \{ v_i, \ldots, v_n \} $}. It turns out that if we take {$P$} as a graph with maximum independent set size no greater than {$k$}, then this definition gives a natural generalization of both chordal graphs and {$ (k + 1) $}-claw-free graphs. We refer to such graphs as inductive {$k$}-independent graphs. We study properties of such families of graphs, and we show that several natural classes of graphs are inductive $k$-independent for small $k$. In particular, any intersection graph of translates of a convex object in a two dimensional plane is an inductive $3$-independent graph; furthermore, any planar graph is an inductive $3$-independent graph. For any fixed constant $k$, we develop simple, polynomial time approximation algorithms for inductive $k$-independent graphs with respect to several well-studied NP-complete problems. Our generalized formulation unifies and extends several previously known results.", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Fischer:2012:QCT, author = "Eldar Fischer and Oded Lachish and Arie Matsliah and Ilan Newman and Orly Yahalom", title = "On the query complexity of testing orientations for being {Eulerian}", journal = j-TALG, volume = "8", number = "2", pages = "15:1--15:??", month = apr, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2151171.2151178", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:57 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider testing directed graphs Eulerianity in the orientation model introduced in Halevy et al. [2005]. Despite the local nature of the Eulerian property, it turns out to be significantly harder to test than other properties studied in the orientation model. We show a nonconstant lower bound on the query complexity of $2$-sided tests and a linear lower bound on the query complexity of $1$-sided tests for this property. On the positive side, we give several $1$-sided and $2$-sided tests, including a sublinear query complexity $2$-sided test, for general graphs. For special classes of graphs, including bounded-degree graphs and expander graphs, we provide improved results. In particular, we give a $2$-sided test with constant query complexity for dense graphs, as well as for expander graphs with a constant expansion parameter.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Fujito:2012:HTM, author = "Toshihiro Fujito", title = "How to trim a {MST}: a $2$-approximation algorithm for minimum cost-tree cover", journal = j-TALG, volume = "8", number = "2", pages = "16:1--16:??", month = apr, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2151171.2151179", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:57 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The minimum cost-tree cover problem is to compute a minimum cost-tree {$T$} in a given connected graph {$G$} with costs on the edges, such that the vertices spanned by {$T$} form a vertex cover for {$G$}. The problem is supposed to occur in applications of vertex cover and in edge-dominating sets when additional connectivity is required for solutions. Whereas a linear-time {$2$}-approximation algorithm for the unweighted case has been known for quite a while, the best approximation ratio known for the weighted case is {$3$}. Moreover, the {$3$}-approximation algorithms for such cases are far from practical due to their inefficiency. In this article we present a fast, purely combinatorial $2$-approximation algorithm for the minimum cost-tree cover problem. It constructs a good approximate solution by trimming some leaves within a minimum spanning tree (MST); and, to determine which leaves to trim, it uses both the primal-dual schema and an instance layering technique adapted from the local ratio method.", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Manthey:2012:AMT, author = "Bodo Manthey", title = "On approximating multicriteria {TSP}", journal = j-TALG, volume = "8", number = "2", pages = "17:1--17:??", month = apr, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2151171.2151180", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:57 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present approximation algorithms for almost all variants of the multicriteria traveling salesman problem (TSP). First, we devise randomized approximation algorithms for multicriteria maximum traveling salesman problems (Max-TSP). For multicriteria Max-STSP where the edge weights have to be symmetric, we devise an algorithm with an approximation ratio of $ 2 / 3 - \epsilon $ . For multicriteria Max-ATSP where the edge weights may be asymmetric, we present an algorithm with a ratio of $ 1 / 2 - \epsilon $. Our algorithms work for any fixed number $k$ of objectives. Furthermore, we present a deterministic algorithm for bicriteria Max-STSP that achieves an approximation ratio of $ 7 / 27 $. Finally, we present a randomized approximation algorithm for the asymmetric multicriteria minimum TSP with triangle inequality (Min-ATSP). This algorithm achieves a ratio of $ \log n + \epsilon $.", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bjorklund:2012:TSP, author = "Andreas Bj{\"o}rklund and Thore Husfeldt and Petteri Kaski and Mikko Koivisto", title = "The traveling salesman problem in bounded degree graphs", journal = j-TALG, volume = "8", number = "2", pages = "18:1--18:??", month = apr, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2151171.2151181", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:57 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show that the traveling salesman problem in bounded-degree graphs can be solved in time {$ O((2 - \epsilon)^n) $}, where {$ \epsilon > 0 $} depends only on the degree bound but not on the number of cities, {$n$}. The algorithm is a variant of the classical dynamic programming solution due to Bellman, and, independently, Held and Karp. In the case of bounded integer weights on the edges, we also give a polynomial-space algorithm with running time {$ O((2 - \epsilon)^n) $} on bounded-degree graphs. In addition, we present an analogous analysis of Ryser's algorithm for the permanent of matrices with a bounded number of nonzero entries in each column.", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Krokhin:2012:HLW, author = "Andrei Krokhin and D{\'a}niel Marx", title = "On the hardness of losing weight", journal = j-TALG, volume = "8", number = "2", pages = "19:1--19:??", month = apr, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2151171.2151182", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:57 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the complexity of local search for the Boolean constraint satisfaction problem (CSP), in the following form: given a CSP instance, that is, a collection of constraints, and a solution to it, the question is whether there is a better (lighter, i.e., having strictly less Hamming weight) solution within a given distance from the initial solution. We classify the complexity, both classical and parameterized, of such problems by a Schaefer-style dichotomy result, that is, with a restricted set of allowed types of constraints. Our results show that there is a considerable amount of such problems that are NP-hard, but fixed-parameter tractable when parameterized by the distance.", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bateni:2012:APC, author = "Mohammadhossein Bateni and Mohammadtaghi Hajiaghayi", title = "Assignment problem in content distribution networks: {Unsplittable} hard-capacitated facility location", journal = j-TALG, volume = "8", number = "3", pages = "20:1--20:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229164", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In a Content Distribution Network (CDN), there are m servers storing the data; each of them has a specific bandwidth. All the requests from a particular client should be assigned to one server because of the routing protocol used. The goal is to minimize the total cost of these assignments-cost of each is proportional to the distance between the client and the server as well as the request size-while the load on each server is kept below its bandwidth limit. When each server also has a setup cost, this is an unsplittable hard-capacitated facility location problem. As much attention as facility location problems have received, there has been no nontrivial approximation algorithm when we have hard capacities (i.e., there can only be one copy of each facility whose capacity cannot be violated) and demands are unsplittable (i.e., all the demand from a client has to be assigned to a single facility). We observe it is NP-hard to approximate the cost to within any bounded factor in this case. Thus, for an arbitrary constant $ \epsilon > 0 $, we relax the capacities to a $ 1 + \epsilon $ factor. For the case where capacities are almost uniform, we give a bicriteria {$ O(\log n, 1 + \epsilon) $}-approximation algorithm for general metrics and a {$ (1 + \epsilon, 1 + \epsilon) $}-approximation algorithm for tree metrics. A bicriteria {$ (\alpha, \beta) $}-approximation algorithm produces a solution of cost at most {$ \alpha $} times the optimum, while violating the capacities by no more than a $ \beta $ factor. We can get the same guarantees for nonuniform capacities if we allow quasipolynomial running time. In our algorithm, some clients guess the facility they are assigned to, and facilities decide the size of the clients they serve. A straightforward approach results in exponential running time. When costs do not satisfy metricity, we show that a 1.5 violation of capacities is necessary to obtain any approximation. It is worth noting that our results generalize bin packing (zero connection costs and facility costs equal to one), knapsack (single facility with all costs being zero), minimum makespan scheduling for related machines (all connection costs being zero), and some facility location problems.", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Panconesi:2012:EPS, author = "Alessandro Panconesi and Jaikumar Radhakrishnan", title = "Expansion properties of (secure) wireless networks", journal = j-TALG, volume = "8", number = "3", pages = "21:1--21:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229165", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show that some topologies arising naturally in the context of wireless networking are low-degree, expander graphs.", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Meyer:2012:ESP, author = "Ulrich Meyer and Norbert Zeh", title = "{I/O}-efficient shortest path algorithms for undirected graphs with random or bounded edge lengths", journal = j-TALG, volume = "8", number = "3", pages = "22:1--22:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229166", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present I/O-efficient single-source shortest path algorithms for undirected graphs. Our main result is an algorithm with I/O complexity {$ O(\sqrt (n m \log L) / B + {\rm MST}(n, m)) $} on graphs with {$n$} vertices, {$m$} edges, and arbitrary edge lengths between {$1$} and {$L$}; {$ {\rm MST}(n, m) $} denotes the I/O complexity of computing a minimum spanning tree; {$B$} denotes the disk block size. If the edge lengths are drawn uniformly at random from $ (0, 1] $, the expected I/O complexity of the algorithm is $ O(\sqrt n m / B + (m / B) \log B + {\rm MST}(n, m)) $. A simpler algorithm has expected I/O complexity $ O(\sqrt (n m \log B) / B + {\rm MST}(n, m)) $ for uniformly random edge lengths.", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chekuri:2012:IAO, author = "Chandra Chekuri and Nitish Korula and Martin P{\'a}l", title = "Improved algorithms for orienteering and related problems", journal = j-TALG, volume = "8", number = "3", pages = "23:1--23:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229167", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we consider the orienteering problem in undirected and directed graphs and obtain improved approximation algorithms. The point to point-orienteering problem is the following: Given an edge-weighted graph {$ G = (V, E) $} (directed or undirected), two nodes {$ s, t \in V $} and a time limit {$B$}, find an {$s$}--{$t$} walk in {$G$} of total length at most {$B$} that maximizes the number of distinct nodes visited by the walk. This problem is closely related to tour problems such as TSP as well as network design problems such as {$k$}-MST. Orienteering with time-windows is the more general problem in which each node {$v$} has a specified time-window {$ [R(v), D(v)] $} and a node {$v$} is counted as visited by the walk only if {$v$} is visited during its time-window. We design new and improved algorithms for the orienteering problem and orienteering with time-windows. Our main results are the following: --- A {$ (2 + \epsilon) $} approximation for orienteering in undirected graphs, improving upon the $3$-approximation of Bansal et al. [2004]. --- An {$ O(\log^2 {\rm OPT}) $} approximation for orienteering in directed graphs, where {$ {\rm OPT} \leq n $} is the number of vertices visited by an optimal solution. Previously, only a quasipolynomial-time algorithm due to Chekuri and P{\'a}l [2005] achieved a polylogarithmic approximation (a ratio of {$ O(\log {\rm OPT}) $}). --- Given an {$ \alpha $} approximation for orienteering, we show an {$ O(\alpha c \{ {\rm maxlog} {\rm OPT}, \log l_{\rm max} / l_{\rm min} \}) $} approximation for orienteering with time-windows, where {$ l_{\rm max} $} and {$ l_{\rm min} $} are the lengths of the longest and shortest time-windows respectively.", acknowledgement = ack-nhfb, articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Asadpour:2012:SCM, author = "Arash Asadpour and Uriel Feige and Amin Saberi", title = "{Santa Claus} meets hypergraph matchings", journal = j-TALG, volume = "8", number = "3", pages = "24:1--24:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229168", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the restricted assignment version of the problem of max-min fair allocation of indivisible goods, also known as the Santa Claus problem. There are $m$ items and $n$ players. Every item has some nonnegative value, and every player is interested in only some of the items. The goal is to distribute the items to the players in a way that maximizes the minimum of the sum of the values of the items given to any player. It was previously shown via a nonconstructive proof that uses the Lov{\'a}sz local lemma that the integrality gap of a certain configuration LP for the problem is no worse than some (unspecified) constant. This gives a polynomial-time algorithm to estimate the optimum value of the problem within a constant factor, but does not provide a polynomial-time algorithm for finding a corresponding allocation. We use a different approach to analyze the integrality gap. Our approach is based upon local search techniques for finding perfect matchings in certain classes of hypergraphs. As a result, we prove that the integrality gap of the configuration LP is no worse than $ 1 / 4 $. Our proof provides a local search algorithm which finds the corresponding allocation, but is nonconstructive in the sense that this algorithm is not known to converge to a local optimum in a polynomial number of steps.", acknowledgement = ack-nhfb, articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Fanelli:2012:SCC, author = "Angelo Fanelli and Michele Flammini and Luca Moscardelli", title = "The speed of convergence in congestion games under best-response dynamics", journal = j-TALG, volume = "8", number = "3", pages = "25:1--25:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229169", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We investigate the speed of convergence of best response dynamics to approximately optimal solutions in congestion games with linear delay functions. In Ackermann et al. [2008] it has been shown that the convergence time of such dynamics to Nash equilibrium may be exponential in the number of players $n$. Motivated by such a negative result, we focus on the study of the states (not necessarily being equilibria) reached after a limited number of players' selfish moves, and we show that {$ \Theta (n \log \log n) $} best responses are necessary and sufficient to achieve states that approximate the optimal solution by a constant factor, under the assumption that every {$ O(n) $} steps each player performs a constant (and nonnull) number of best responses. We show that such result is tight also for the simplest case of singleton congestion games.", acknowledgement = ack-nhfb, articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Baptiste:2012:PTA, author = "Philippe Baptiste and Marek Chrobak and Christoph D{\"u}rr", title = "Polynomial-time algorithms for minimum energy scheduling", journal = j-TALG, volume = "8", number = "3", pages = "26:1--26:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229170", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The aim of power management policies is to reduce the amount of energy consumed by computer systems while maintaining a satisfactory level of performance. One common method for saving energy is to simply suspend the system during idle times. No energy is consumed in the suspend mode. However, the process of waking up the system itself requires a certain fixed amount of energy, and thus suspending the system is beneficial only if the idle time is long enough to compensate for this additional energy expenditure. In the specific problem studied in the article, we have a set of jobs with release times and deadlines that need to be executed on a single processor. Preemptions are allowed. The processor requires energy $L$ to be woken up and, when it is on, it uses one unit of energy per one unit of time. It has been an open problem whether a schedule minimizing the overall energy consumption can be computed in polynomial time. We solve this problem in positive, by providing an {$ O(n^5) $}-time algorithm. In addition we provide an {$ O(n^4) $}-time algorithm for computing the minimum energy schedule when all jobs have unit length.", acknowledgement = ack-nhfb, articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Diedrich:2012:TAA, author = "Florian Diedrich and Klaus Jansen and Lars Pr{\"a}del and Ulrich M. Schwarz and Ola Svensson", title = "Tight approximation algorithms for scheduling with fixed jobs and nonavailability", journal = j-TALG, volume = "8", number = "3", pages = "27:1--27:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229171", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study two closely related problems in nonpreemptive scheduling of jobs on identical parallel machines. In these two settings there are either fixed jobs or nonavailability intervals during which the machines are not available; in both cases, the objective is to minimize the makespan. Both formulations have different applications, for example, in turnaround scheduling or overlay computing. For both problems we contribute approximation algorithms with an improved ratio of $ 3 / 2 $. For scheduling with fixed jobs, a lower bound of $ 3 / 2 $ on the approximation ratio has been obtained by Scharbrodt et al. [1999]; for scheduling with nonavailability we provide the same lower bound. We use dual approximation, creation of a gap structure, and a PTAS for the multiple subset sum problem, combined with a postprocessing step to assign large jobs.", acknowledgement = ack-nhfb, articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Edmonds:2012:SSP, author = "Jeff Edmonds and Kirk Pruhs", title = "Scalably scheduling processes with arbitrary speedup curves", journal = j-TALG, volume = "8", number = "3", pages = "28:1--28:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229172", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give a scalable ($ (1 + \epsilon) $-speed {$ O(1) $}-competitive) nonclairvoyant algorithm for scheduling jobs with sublinear nondecreasing speedup curves on multiple processors with the objective of average response time.", acknowledgement = ack-nhfb, articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Collette:2012:ETP, author = "S{\'e}bastien Collette and Vida Dujmovi{\'c} and John Iacono and Stefan Langerman and Pat Morin", title = "Entropy, triangulation, and point location in planar subdivisions", journal = j-TALG, volume = "8", number = "3", pages = "29:1--29:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229173", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A data structure is presented for point location in connected planar subdivisions when the distribution of queries is known in advance. The data structure has an expected query time that is within a constant factor of optimal. More specifically, an algorithm is presented that preprocesses a connected planar subdivision {$G$} of size {$n$} and a query distribution {$D$} to produce a point location data structure for {$G$}. The expected number of point-line comparisons performed by this data structure, when the queries are distributed according to {$D$}, is {$ \tilde {H} + O(\tilde {H}^{1 / 2} + 1) $} where {$ \tilde {H} = \tilde {H}(G, D) $} is a lower bound on the expected number of point-line comparisons performed by any linear decision tree for point location in {$G$} under the query distribution {$D$}. The preprocessing algorithm runs in {$ O(n \log n) $} time and produces a data structure of size {$ O(n) $}. These results are obtained by creating a Steiner triangulation of {$G$} that has near-minimum entropy.", acknowledgement = ack-nhfb, articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Damerow:2012:SAL, author = "Valentina Damerow and Bodo Manthey and Friedhelm {Meyer Auf Der Heide} and Harald R{\"a}cke and Christian Scheideler and Christian Sohler and Till Tantau", title = "Smoothed analysis of left-to-right maxima with applications", journal = j-TALG, volume = "8", number = "3", pages = "30:1--30:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229174", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A left-to-right maximum in a sequence of $n$ numbers $ s_1 $, \ldots {}, $ s_n $ is a number that is strictly larger than all preceding numbers. In this article we present a smoothed analysis of the number of left-to-right maxima in the presence of additive random noise. We show that for every sequence of $n$ numbers $ s_i \in [0, 1] $ that are perturbed by uniform noise from the interval $ [ - \epsilon, \epsilon] $, the expected number of left-to-right maxima is {$ \Theta (\sqrt n / \epsilon + \log n) $} for {$ \epsilon > 1 / n $}. For Gaussian noise with standard deviation {$ \sigma $} we obtain a bound of {$ O((\log^{3 / 2} n) / \sigma + \log n) $}. We apply our results to the analysis of the smoothed height of binary search trees and the smoothed number of comparisons in the quicksort algorithm and prove bounds of {$ \Theta (\sqrt n / \epsilon + \log n) $} and {$ \Theta (n / \epsilon + 1 \sqrt n / \epsilon + n \log n) $}, respectively, for uniform random noise from the interval {$ [ - \epsilon, \epsilon] $}. Our results can also be applied to bound the smoothed number of points on a convex hull of points in the two-dimensional plane and to smoothed motion complexity, a concept we describe in this article. We bound how often one needs to update a data structure storing the smallest axis-aligned box enclosing a set of points moving in d -dimensional space.", acknowledgement = ack-nhfb, articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bassino:2012:COF, author = "Fr{\'e}d{\'e}rique Bassino and Julien Cl{\'e}ment and Pierre Nicod{\`e}me", title = "Counting occurrences for a finite set of words: combinatorial methods", journal = j-TALG, volume = "8", number = "3", pages = "31:1--31:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229175", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we provide the multivariate generating function counting texts according to their length and to the number of occurrences of words from a finite set. The application of the inclusion-exclusion principle to word counting due to Goulden and Jackson [1979, 1983] is used to derive the result. Unlike some other techniques which suppose that the set of words is reduced (i.e., where no two words are factor of one another), the finite set can be chosen arbitrarily. Noonan and Zeilberger [1999] already provided a Maple package treating the nonreduced case, without giving an expression of the generating function or a detailed proof. We provide a complete proof validating the use of the inclusion-exclusion principle. Some formul{\ae} for expected values, variance, and covariance for number of occurrences when considering two arbitrary sets of finite words are given as an application of our methodology.", acknowledgement = ack-nhfb, articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Arvind:2012:TNG, author = "V. Arvind and Piyush P. Kurur", title = "Testing nilpotence of {Galois} groups in polynomial time", journal = j-TALG, volume = "8", number = "3", pages = "32:1--32:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229176", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give the first polynomial-time algorithm for checking whether the Galois group {$ {\rm Gal}(f) $} of an input polynomial {$ f(X) \in Q[X] $} is nilpotent: the running time of our algorithm is bounded by a polynomial in the size of the coefficients of {$f$} and the degree of {$f$}. Additionally, we give a deterministic polynomial-time algorithm that, when given as input a polynomial {$ f(X) \in Q[X] $} with nilpotent Galois group, computes for each prime factor {$p$} of {$ \# {\rm Gal}(f) $}, a polynomial {$ g_p(X) \in Q[X] $} whose Galois group of is the {$p$}-Sylow subgroup of {$ {\rm Gal}(f) $}.", acknowledgement = ack-nhfb, articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Roditty:2012:RPS, author = "Liam Roditty and Uri Zwick", title = "Replacement paths and $k$ simple shortest paths in unweighted directed graphs", journal = j-TALG, volume = "8", number = "4", pages = "33:1--33:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344423", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Let {$ G = (V, E) $} be a directed graph and let {$P$} be a shortest path from {$s$} to {$t$} in {$G$}. In the replacement paths problem, we are required to find, for every edge {$e$} on {$P$}, a shortest path from {$s$} to {$t$} in {$G$} that avoids {$e$}. The only known algorithm for solving the problem, even for unweighted directed graphs, is the trivial algorithm in which each edge on the path, in its turn, is excluded from the graph and a shortest paths tree is computed from {$s$}. The running time is {$ O(m n + n^2 \log n) $}. The replacement paths problem is strongly motivated by two different applications: (1) The fastest algorithm to compute the {$k$} simple shortest paths between {$s$} and {$t$} in directed graphs [Yen 1971; Lawler 1972] computes the replacement paths between $s$ and $t$. Its running time is {$ \tilde {O}(m n k) $}. (2) The replacement paths problem is used to compute the Vickrey pricing of edges in a distributed network. It was raised as an open problem by Nisan and Ronen [2001] whether it is possible to compute the Vickrey pricing faster than {$n$} computations of a shortest paths tree. In this article we present the first nontrivial algorithm for computing replacement paths in unweighted directed graphs (and in graphs with small integer weights). Our algorithm is Monte-Carlo and its running time is {$ \tilde {O}(m \sqrt n) $}. This result immediately improves the running time of the two applications mentioned above in a factor of {$ \sqrt n $}. We also show how to reduce the problem of computing {$k$} simple shortest paths between {$s$} and $t$ to {$ O(k) $} computations of a second simple shortest path from {$s$} to {$t$} each time in a different subgraph of {$G$}. The importance of this result is that computing a second simple shortest path may turn out to be an easier problem than computing the replacement paths, thus, we can focus our efforts to improve the k simple shortest paths algorithm in obtaining a faster algorithm for the second shortest path problem.", acknowledgement = ack-nhfb, articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chan:2012:APS, author = "Timothy M. Chan", title = "All-pairs shortest paths for unweighted undirected graphs in $ o(m n) $ time", journal = j-TALG, volume = "8", number = "4", pages = "34:1--34:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344424", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We revisit the all-pairs-shortest-paths problem for an unweighted undirected graph with $n$ vertices and $m$ edges. We present new algorithms with the following running times: {$ O(m n / \log n) $} if {$ m > n \log n \log \log \log n O(m n \log \log n / \log n) $} if {$ m > n \log \log n O(n^2 \log^2 \log n / \log n) $} if {$ m \leq n \log \log n $}. These represent the best time bounds known for the problem for all {$ m \ll n^{1.376} $} . We also obtain a similar type of result for the diameter problem for unweighted directed graphs.", acknowledgement = ack-nhfb, articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Baswana:2012:FDR, author = "Surender Baswana and Sumeet Khurana and Soumojit Sarkar", title = "Fully dynamic randomized algorithms for graph spanners", journal = j-TALG, volume = "8", number = "4", pages = "35:1--35:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344425", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Spanner of an undirected graph {$ G = (V, E) $} is a subgraph that is sparse and yet preserves all-pairs distances approximately. More formally, a spanner with stretch {$ t \in N $} is a subgraph {$ (V, E_S) $}, {E$_S \subseteq E$} such that the distance between any two vertices in the subgraph is at most {$t$} times their distance in {$G$}. Though {$G$} is trivially a {$t$}-spanner of itself, the research as well as applications of spanners invariably deal with a {$t$}-spanner that has as small number of edges as possible. We present fully dynamic algorithms for maintaining spanners in centralized as well as synchronized distributed environments. These algorithms are designed for undirected unweighted graphs and use randomization in a crucial manner. Our algorithms significantly improve the existing fully dynamic algorithms for graph spanners. The expected size (number of edges) of a {$t$}-spanner maintained at each stage by our algorithms matches, up to a polylogarithmic factor, the worst case optimal size of a $t$-spanner. The expected amortized time (or messages communicated in distributed environment) to process a single insertion\slash deletion of an edge by our algorithms is close to optimal.", acknowledgement = ack-nhfb, articleno = "35", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Swamy:2012:ESS, author = "Chaitanya Swamy", title = "The effectiveness of {Stackelberg} strategies and tolls for network congestion games", journal = j-TALG, volume = "8", number = "4", pages = "36:1--36:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344426", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "It is well known that in a network with arbitrary (convex) latency functions that are a function of edge traffic, the worst-case ratio, over all inputs, of the system delay caused due to selfish behavior versus the system delay of the optimal centralized solution may be unbounded even if the system consists of only two parallel links. This ratio is called the price of anarchy (PoA). In this article, we investigate ways by which one can reduce the performance degradation due to selfish behavior. We investigate two primary methods (a) Stackelberg routing strategies, where a central authority, for example, network manager, controls a fixed fraction of the flow, and can route this flow in any desired way so as to influence the flow of selfish users; and (b) network tolls, where tolls are imposed on the edges to modify the latencies of the edges, and thereby influence the induced Nash equilibrium. We obtain results demonstrating the effectiveness of both Stackelberg strategies and tolls in controlling the price of anarchy. For Stackelberg strategies, we obtain the first results for nonatomic routing in graphs more general than parallel-link graphs, and strengthen existing results for parallel-link graphs. (i) In series-parallel graphs, we show that Stackelberg routing reduces the PoA to a constant (depending on the fraction of flow controlled). (ii) For general graphs, we obtain latency-class specific bounds on the PoA with Stackelberg routing, which give a continuous trade-off between the fraction of flow controlled and the price of anarchy. (iii) In parallel-link graphs, we show that for any given class L of latency functions, Stackelberg routing reduces the PoA to at most {$ \alpha + (1 - \alpha) c \rho (L) $}, where {$ \alpha $} is the fraction of flow controlled and {$ \rho (L) $} is the PoA of class {$L$} (when {$ \alpha = 0 $}). For network tolls, motivated by the known strong results for nonatomic games, we consider the more general setting of atomic splittable routing games. We show that tolls inducing an optimal flow always exist, even for general asymmetric games with heterogeneous users, and can be computed efficiently by solving a convex program. This resolves a basic open question about the effectiveness of tolls for atomic splittable games. Furthermore, we give a complete characterization of flows that can be induced via tolls.", acknowledgement = ack-nhfb, articleno = "36", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Czyzowicz:2012:HMA, author = "Jurek Czyzowicz and Andrzej Pelc and Arnaud Labourel", title = "How to meet asynchronously (almost) everywhere", journal = j-TALG, volume = "8", number = "4", pages = "37:1--37:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344427", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Two mobile agents (robots) with distinct labels have to meet in an arbitrary, possibly infinite, unknown connected graph or in an unknown connected terrain in the plane. Agents are modeled as points, and the route of each of them only depends on its label and on the unknown environment. The actual walk of each agent also depends on an asynchronous adversary that may arbitrarily vary the speed of the agent, stop it, or even move it back and forth, as long as the walk of the agent is continuous, does not leave its route and covers all of it. Meeting in a graph means that both agents must be at the same time in some node or in some point inside an edge of the graph, while meeting in a terrain means that both agents must be at the same time in some point of the terrain. Does there exist a deterministic algorithm that allows any two agents to meet in any unknown environment in spite of this very powerful adversary? We give deterministic rendezvous algorithms for agents starting at arbitrary nodes of any anonymous connected graph (finite or infinite) and for agents starting at any interior points with rational coordinates in any closed region of the plane with path-connected interior. In the geometric scenario agents may have different compasses and different units of length. While our algorithms work in a very general setting --- agents can, indeed, meet almost everywhere --- we show that none of these few limitations imposed on the environment can be removed. On the other hand, our algorithm also guarantees the following approximate rendezvous for agents starting at arbitrary interior points of a terrain as previously stated agents will eventually get to within an arbitrarily small positive distance from each other.", acknowledgement = ack-nhfb, articleno = "37", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Binkele-Raible:2012:KPN, author = "Daniel Binkele-Raible and Henning Fernau and Fedor V. Fomin and Daniel Lokshtanov and Saket Saurabh and Yngve Villanger", title = "Kernel(s) for problems with no kernel: On out-trees with many leaves", journal = j-TALG, volume = "8", number = "4", pages = "38:1--38:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344428", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The $k$-Leaf Out-Branching problem is to find an out-branching, that is a rooted oriented spanning tree, with at least k leaves in a given digraph. The problem has recently received much attention from the viewpoint of parameterized algorithms. Here, we take a kernelization based approach to the $k$-Leaf-Out-Branching problem. We give the first polynomial kernel for Rooted $k$-Leaf-Out-Branching, a variant of $k$-Leaf-Out-Branching where the root of the tree searched for is also a part of the input. Our kernel with O(k$^3$) vertices is obtained using extremal combinatorics. For the $k$-Leaf-Out-Branching problem, we show that no polynomial-sized kernel is possible unless coNP is in NP/poly. However, our positive results for Rooted $k$-Leaf-Out-Branching immediately imply that the seemingly intractable k Leaf-Out-Branching problem admits a data reduction to $n$ independent polynomial-sized kernels. These two results, tractability and intractability side by side, are the first ones separating Karp kernelization from Turing kernelization. This answers affirmatively an open problem regarding ``cheat kernelization'' raised by Mike Fellows and Jiong Guo independently.", acknowledgement = ack-nhfb, articleno = "38", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Im:2012:OSA, author = "Sungjin Im and Benjamin Moseley", title = "An online scalable algorithm for average flow time in broadcast scheduling", journal = j-TALG, volume = "8", number = "4", pages = "39:1--39:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344429", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, the online pull-based broadcast model is considered. In this model, there are $n$ pages of data stored at a server and requests arrive for pages online. When the server broadcasts page p, all outstanding requests for the same page p are simultaneously satisfied. We consider the problem of minimizing average (total) flow time online where all pages are unit-sized. For this problem, there has been a decade-long search for an online algorithm which is scalable, that is, $ (1 + \epsilon) $-speed {$ O(1) $}-competitive for any fixed {$ \epsilon > 0 $}. In this article, we give the first analysis of an online scalable algorithm.", acknowledgement = ack-nhfb, articleno = "39", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Karakostas:2012:FMT, author = "George Karakostas and Stavros G. Kolliopoulos and Jing Wang", title = "An {FPTAS} for the minimum total weighted tardiness problem with a fixed number of distinct due dates", journal = j-TALG, volume = "8", number = "4", pages = "40:1--40:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344430", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a sequencing of jobs on a single machine, each one with a weight, processing time, and a due date, the tardiness of a job is the time needed for its completion beyond its due date. We present an FPTAS for the basic scheduling problem of minimizing the total weighted tardiness when the number of distinct due dates is fixed. Previously, an FPTAS was known only for the case where all jobs have a common due date.", acknowledgement = ack-nhfb, articleno = "40", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Deshpande:2012:PPF, author = "Amol Deshpande and Lisa Hellerstein", title = "Parallel pipelined filter ordering with precedence constraints", journal = j-TALG, volume = "8", number = "4", pages = "41:1--41:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344431", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the parallel pipelined filter ordering problem, we are given a set of $n$ filters that run in parallel. The filters need to be applied to a stream of elements, to determine which elements pass all filters. Each filter has a rate limit r$_i$ on the number of elements it can process per unit time, and a selectivity p$_i$, which is the probability that a random element will pass the filter. The goal is to maximize throughput. This problem appears naturally in a variety of settings, including parallel query optimization in databases and query processing over Web services. We present an O(n$^3$) algorithm for this problem, given tree-structured precedence constraints on the filters. This extends work of Condon et al. [2009] and Kodialam [2001], who presented algorithms for solving the problem without precedence constraints. Our algorithm is combinatorial and produces a sparse solution. Motivated by join operators in database queries, we also give algorithms for versions of the problem in which ``filter'' selectivities may be greater than or equal to 1. We prove a strong connection between the more classical problem of minimizing total work in sequential filter ordering (A), and the parallel pipelined filter ordering problem (B). More precisely, we prove that A is solvable in polynomial time for a given class of precedence constraints if and only if B is as well. This equivalence allows us to show that B is NP-Hard in the presence of arbitrary precedence constraints (since A is known to be NP-Hard in that setting).", acknowledgement = ack-nhfb, articleno = "41", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{He:2012:SOT, author = "Meng He and J. Ian Munro and Srinivasa Rao Satti", title = "Succinct ordinal trees based on tree covering", journal = j-TALG, volume = "8", number = "4", pages = "42:1--42:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344432", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Various methods have been used to represent a tree on $n$ nodes in essentially the information-theoretic minimum space while supporting various navigational operations in constant time, but different representations usually support different operations. Our main contribution is a succinct representation of ordinal trees, based on that of Geary et al. [2006], that supports all the navigational operations supported by various succinct tree representations while requiring only 2 n + o (n) bits. It also supports efficient level-order traversal, a useful ordering previously supported only with a very limited set of operations. Our second contribution expands on the notion of a single succinct representation supporting more than one traversal ordering, by showing that our method supports two other encoding schemes as abstract data types. In particular, it supports extracting a word ({$ O(\lg n) $} bits) of the balanced parenthesis sequence or depth first unary degree sequence in {$ O(f (n)) $} time, using at most {$ n / f (n) + o (n) $} additional bits, for any {$ f(n) $} in {$ O(\lg n) $} and {$ \Omega (1) $}.", acknowledgement = ack-nhfb, articleno = "42", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Agarwal:2012:RSU, author = "Pankaj K. Agarwal and Siu-Wing Cheng and Ke Yi", title = "Range searching on uncertain data", journal = j-TALG, volume = "8", number = "4", pages = "43:1--43:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344433", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Querying uncertain data has emerged as an important problem in data management due to the imprecise nature of many measurement data. In this article, we study answering range queries over uncertain data. Specifically, we are given a collection {$P$} of {$n$} uncertain points in {$R$}, each represented by its one-dimensional probability density function (pdf). The goal is to build a data structure on {$P$} such that, given a query interval {$I$} and a probability threshold {$ \tau $}, we can quickly report all points of {$P$} that lie in {$I$} with probability at least {$ \tau $}. We present various structures with linear or near-linear space and (poly)logarithmic query time. Our structures support pdf's that are either histograms or more complex ones such as Gaussian or piecewise algebraic.", acknowledgement = ack-nhfb, articleno = "43", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Andoni:2012:SCE, author = "Alexandr Andoni and Robert Krauthgamer", title = "The smoothed complexity of edit distance", journal = j-TALG, volume = "8", number = "4", pages = "44:1--44:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344434", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We initiate the study of the smoothed complexity of sequence alignment, by proposing a semi-random model of edit distance between two input strings, generated as follows: First, an adversary chooses two binary strings of length d and a longest common subsequence A of them. Then, every character is perturbed independently with probability p, except that A is perturbed in exactly the same way inside the two strings. We design two efficient algorithms that compute the edit distance on smoothed instances up to a constant factor approximation. The first algorithm runs in near-linear time, namely d$^{{1 + \epsilon }}$ for any fixed $ \epsilon > 0 $. The second one runs in time sublinear in $d$, assuming the edit distance is not too small. These approximation and runtime guarantees are significantly better than the bounds that were known for worst-case inputs. Our technical contribution is twofold. First, we rely on finding matches between substrings in the two strings, where two substrings are considered a match if their edit distance is relatively small, a prevailing technique in commonly used heuristics, such as PatternHunter of Ma et al. [2002]. Second, we effectively reduce the smoothed edit distance to a simpler variant of (worst-case) edit distance, namely, edit distance on permutations (a.k.a. Ulam's metric). We are thus able to build on algorithms developed for the Ulam metric, whose much better algorithmic guarantees usually do not carry over to general edit distance.", acknowledgement = ack-nhfb, articleno = "44", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Nutov:2012:AMC, author = "Zeev Nutov", title = "Approximating minimum-cost connectivity problems via uncrossable bifamilies", journal = j-TALG, volume = "9", number = "1", pages = "1:1--1:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390177", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give approximation algorithms for the Survivable Network problem. The input consists of a graph $ G = (V, E) $ with edge/node-costs, a node subset $ S \subseteq V $, and connectivity requirements $ \{ r(s, t) : s, t \in T \subseteq V \} $. The goal is to find a minimum cost subgraph $H$ of $G$ that for all $ s, t \in T $ contains $ r(s, t) $ pairwise edge-disjoint $ s t $-paths such that no two of them have a node in $ S \{ s, t \} $ in common. Three extensively studied particular cases are: Edge-Connectivity Survivable Network ($ S = \oslash $), Node-Connectivity Survivable Network ($ S = V $), and Element-Connectivity Survivable Network ($ r(s, t) = 0 $ whenever $ s \in S $ or $ t \in S $). Let $ k = \max \{_{s, t \in T} \} r(s, t) $. In Rooted Survivable Network, there is $ s \in T $ such that $ r(u, t) = 0 $ for all $ u \neq s $, and in the Subset $k$-Connected Subgraph problem $ r(s, t) = k $ for all $ s, t \in T $. For edge-costs, our ratios are $ O(k \log k) $ for Rooted Survivable Network and $ O(k^2 \log k) $ for Subset $k$-Connected Subgraph. This improves the previous ratio $ O(k^2 \log n) $, and for constant values of $k$ settles the approximability of these problems to a constant. For node-costs, our ratios are as follows. --- $ O(k \log | T |) $ for Element-Connectivity Survivable Network, matching the best known ratio for Edge-Connectivity Survivable Network. --- $ O(k^2 \log | T |) $ for Rooted Survivable Network and $ O(k^3 \log | T |) $ for Subset $k$-Connected Subgraph, improving the ratio $ O(k^8 \log^2 | T |) $. --- $ O(k^4 \log^2 | T |) $ for Survivable Network; this is the first nontrivial approximation algorithm for the node-costs version of the problem.", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hajiaghayi:2012:PCS, author = "Mohammadtaghi Hajiaghayi and Rohit Khandekar and Guy Kortsarz and Zeev Nutov", title = "Prize-collecting {Steiner} network problems", journal = j-TALG, volume = "9", number = "1", pages = "2:1--2:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390178", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the Steiner Network problem, we are given a graph {$G$} with edge-costs and connectivity requirements {$ r_{u v} $} between node pairs {$ u, v $}. The goal is to find a minimum-cost subgraph {$H$} of {$G$} that contains {$ r_{uv} $} edge-disjoint paths for all {$ u, v \in V $}. In Prize-Collecting Steiner Network problems, we do not need to satisfy all requirements, but are given a penalty function for violating the connectivity requirements, and the goal is to find a subgraph {$H$} that minimizes the cost plus the penalty. The case when {$ r_{uv} \in \{ 0, 1 \} $} is the classic Prize-Collecting Steiner Forest problem. In this article, we present a novel linear programming relaxation for the Prize-Collecting Steiner Network problem, and by rounding it, obtain the first constant-factor approximation algorithm for submodular and monotone nondecreasing penalty functions. In particular, our setting includes all-or-nothing penalty functions, which charge the penalty even if the connectivity requirement is slightly violated; this resolves an open question posed by Nagarajan et al. [2008]. We further generalize our results for element-connectivity and node-connectivity.", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Awerbuch:2012:DAM, author = "Baruch Awerbuch and Rohit Khandekar and Satish Rao", title = "Distributed algorithms for multicommodity flow problems via approximate steepest descent framework", journal = j-TALG, volume = "9", number = "1", pages = "3:1--3:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390179", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider solutions for distributed multicommodity flow problems, which are solved by multiple agents operating in a cooperative but uncoordinated manner. We show first distributed solutions that allow $ (1 + \epsilon) $ approximation and whose convergence time is essentially linear in the maximal path length, and is independent of the number of commodities and the size of the graph. Our algorithms use a very natural approximate steepest descent framework, combined with a blocking flow technique to speed up the convergence in distributed and parallel environment. Previously known solutions that achieved comparable convergence time and approximation ratio required exponential computational and space overhead per agent.", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chen:2012:CRS, author = "Wei Chen and Christian Sommer and Shang-Hua Teng and Yajun Wang", title = "A compact routing scheme and approximate distance oracle for power-law graphs", journal = j-TALG, volume = "9", number = "1", pages = "4:1--4:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390180", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Compact routing addresses the tradeoff between table sizes and stretch, which is the worst-case ratio between the length of the path a packet is routed through by the scheme and the length of an actual shortest path from source to destination. We adapt the compact routing scheme by Thorup and Zwick [2001] to optimize it for power-law graphs. We analyze our adapted routing scheme based on the theory of unweighted random power-law graphs with fixed expected degree sequence by Aiello et al. [2000]. Our result is the first analytical bound coupled to the parameter of the power-law graph model for a compact routing scheme. Let $n$ denote the number of nodes in the network. We provide a labeled routing scheme that, after a stretch--5 handshaking step (similar to DNS lookup in TCP/IP), routes messages along stretch--3 paths. We prove that, instead of routing tables with {$ \tilde {O}(n^{1 / 2}) $} bits ({$ \tilde {O} $} suppresses factors logarithmic in {$n$}) as in the general scheme by Thorup and Zwick, expected sizes of {$ O(n^\gamma \log n) $} bits are sufficient, and that all the routing tables can be constructed at once in expected time {$ O(n^{1 + \gamma } \log n) $}, with {$ \gamma = \tau - 22 / \tau - 3 + \epsilon $}, where {$ \tau \in (2, 3) $} is the power-law exponent and {$ \epsilon 0 $} (which implies $ \epsilon < \gamma < 1 / 3 + \epsilon $). Both bounds also hold with probability at least $ 1 - 1 / n $ (independent of $ \epsilon $). The routing scheme is a labeled scheme, requiring a stretch--5 handshaking step. The scheme uses addresses and message headers with {$ O(\log n \log \log n) $} bits, with probability at least {$ 1 - o(1) $}. We further demonstrate the effectiveness of our scheme by simulations on real-world graphs as well as synthetic power-law graphs. With the same techniques as for the compact routing scheme, we also adapt the approximate distance oracle by Thorup and Zwick [2001, 2005] for stretch-3 and we obtain a new upper bound of expected {$ \tilde {O}(n^{1 + \gamma }) $} for space and preprocessing for random power-law graphs. Our distance oracle is the first one optimized for power-law graphs. Furthermore, we provide a linear-space data structure that can answer 5--approximate distance queries in time at most {$ \tilde {O}(n^{1 / 4 + \epsilon }) $} (similar to {$ \gamma $}, the exponent actually depends on {$ \tau $} and lies between {$ \epsilon $} and $ 1 / 4 + \epsilon $).", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Jez:2012:OSP, author = "Lukasz Jez and Fei Li and Jay Sethuraman and Clifford Stein", title = "Online scheduling of packets with agreeable deadlines", journal = j-TALG, volume = "9", number = "1", pages = "5:1--5:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390181", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article concerns an online packet scheduling problem that arises as a natural model for buffer management at a network router. Packets arrive at a router at integer time steps, and are buffered upon arrival. Packets have non-negative weights and integer deadlines that are (weakly) increasing in their arrival times. In each integer time step, at most one packet can be sent. The objective is to maximize the sum of the weights of the packets that are sent by their deadlines. The main results include an optimal $ (\phi := (1 + \sqrt 5) / 2 \approx 1.618) $-competitive deterministic online algorithm, a $ (4 / 3 \approx 1.33) $-competitive randomized online algorithm against an oblivious adversary, and a $2$-speed $1$-competitive deterministic online algorithm. The analysis does not use a potential function explicitly, but instead modifies the adversary's buffer and credits the adversary to account for these modifications.", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bonifaci:2012:ACP, author = "Vincenzo Bonifaci and Ho-Leung Chan and Alberto Marchetti-Spaccamela and Nicole Megow", title = "Algorithms and complexity for periodic real-time scheduling", journal = j-TALG, volume = "9", number = "1", pages = "6:1--6:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390182", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We investigate the preemptive scheduling of periodic tasks with hard deadlines. We show that, even in the uniprocessor case, no pseudopolynomial-time algorithm can test the feasibility of a task system within a constant speedup bound, unless P = NP. This result contrasts with recent results for sporadic task systems. For two special cases, synchronous task systems and systems with a constant number of different task types, we provide the first polynomial-time constant-speedup feasibility tests for multiprocessor platforms. Furthermore, we show that the problem of testing feasibility is coNP-hard for synchronous multiprocessor task systems. The complexity of some of these problems has been open for a long time. We also propose a weight maximization variant of the feasibility problem, where every task has a nonnegative weight, and the goal is to find a subset of tasks that can be scheduled feasibly and has maximum weight. We give the first constant-speed, constant-approximation algorithm for the case of synchronous task systems, together with related hardness results.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Halldorsson:2012:WSP, author = "Magn{\'u}s M. Halld{\'o}rsson", title = "Wireless scheduling with power control", journal = j-TALG, volume = "9", number = "1", pages = "7:1--7:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390183", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the scheduling of arbitrary wireless links in the physical model of interference to minimize the time for satisfying all requests. We study here the combined problem of scheduling and power control, where we seek both an assignment of power settings and a partition of the links so that each set satisfies the signal-to-interference-plus-noise (SINR) constraints. We give an algorithm that attains an approximation ratio of {$ O(\log n c \log \log \Delta) $}, where {$n$} is the number of links and {$ \Delta $} is the ratio between the longest and the shortest link length. Under the natural assumption that lengths are represented in binary, this gives the first approximation ratio that is polylogarithmic in the size of the input. The algorithm has the desirable property of using an oblivious power assignment, where the power assigned to a sender depends only on the length of the link. We give evidence that this dependence on {$ \Delta $} is unavoidable, showing that any reasonably behaving oblivious power assignment results in a {$ \Omega (\log \log \Delta) $}-approximation. These results hold also for the (weighted) capacity problem of finding a maximum (weighted) subset of links that can be scheduled in a single time slot. In addition, we obtain improved approximation for a bidirectional variant of the scheduling problem, give partial answers to questions about the utility of graphs for modeling physical interference, and generalize the setting from the standard {$2$}-dimensional Euclidean plane to doubling metrics. Finally, we explore the utility of graph models in capturing wireless interference.", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ebrahimi:2012:CAW, author = "Javad B. Ebrahimi and Christina Fragouli", title = "Combinatiorial algorithms for wireless information flow", journal = j-TALG, volume = "9", number = "1", pages = "8:1--8:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390184", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A long-standing open question in information theory is to characterize the unicast capacity of a wireless relay network. The difficulty arises due to the complex signal interactions induced in the network, since the wireless channel inherently broadcasts the signals and there is interference among transmissions. Recently, Avestimehr et al. [2007b] proposed a linear deterministic model that takes into account the shared nature of wireless channels, focusing on the signal interactions rather than the background noise. They generalized the min-cut max-flow theorem for graphs to networks of deterministic channels and proved that the capacity can be achieved using information theoretical tools. They showed that the value of the minimum cut is in this case the minimum rank of all the adjacency matrices describing source-destination cuts. In this article, we develop a polynomial-time algorithm that discovers the relay encoding strategy to achieve the min-cut value in linear deterministic (wireless) networks, for the case of a unicast connection. Our algorithm crucially uses a notion of linear independence between channels to calculate the capacity in polynomial time. Moreover, we can achieve the capacity by using very simple one-symbol processing at the intermediate nodes, thereby constructively yielding finite-length strategies that achieve the unicast capacity of the linear deterministic (wireless) relay network.", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chekuri:2012:SMP, author = "Chandra Chekuri and Kenneth L. Clarkson and Sariel Har-Peled", title = "On the set multicover problem in geometric settings", journal = j-TALG, volume = "9", number = "1", pages = "9:1--9:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390185", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the set multicover problem in geometric settings. Given a set of points {$P$} and a collection of geometric shapes (or sets) {$F$}, we wish to find a minimum cardinality subset of {$F$} such that each point {$ p \in P $} is covered by (contained in) at least {$ d(p) $} sets. Here, {$ d(p) $} is an integer demand (requirement) for {$p$}. When the demands $ d(p) = 1 $ for all $p$, this is the standard set cover problem. The set cover problem in geometric settings admits an approximation ratio that is better than that for the general version. In this article, we show that similar improvements can be obtained for the multicover problem as well. In particular, we obtain an {$ O(\log {\rm opt}) $} approximation for set systems of bounded VC-dimension, and an {$ O(1) $} approximation for covering points by half-spaces in three dimensions and for some other classes of shapes.", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Giesen:2012:APC, author = "Joachim Giesen and Martin Jaggi and S{\"o}ren Laue", title = "Approximating parameterized convex optimization problems", journal = j-TALG, volume = "9", number = "1", pages = "10:1--10:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390186", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider parameterized convex optimization problems over the unit simplex, that depend on one parameter. We provide a simple and efficient scheme for maintaining an $ \epsilon $-approximate solution (and a corresponding $ \epsilon $-coreset) along the entire parameter path. We prove correctness and optimality of the method. Practically relevant instances of the abstract parameterized optimization problem are for example regularization paths of support vector machines, multiple kernel learning, and minimum enclosing balls of moving points.", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Philip:2012:PKD, author = "Geevarghese Philip and Venkatesh Raman and Somnath Sikdar", title = "Polynomial kernels for dominating set in graphs of bounded degeneracy and beyond", journal = j-TALG, volume = "9", number = "1", pages = "11:1--11:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390187", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show that for every fixed $ j \geq i \geq 1 $, the $k$-Dominating Set problem restricted to graphs that do not have {$ K_{ij} $} (the complete bipartite graph on {$ (i + j) $} vertices, where the two parts have {$i$} and {$j$} vertices, respectively) as a subgraph is fixed parameter tractable (FPT) and has a polynomial kernel. We describe a polynomial-time algorithm that, given a {$ K_{i, j} $}-free graph {$G$} and a nonnegative integer {$k$}, constructs a graph {$H$} (the ``kernel'') and an integer {$ k' $} such that (1) {$G$} has a dominating set of size at most {$k$} if and only if {$H$} has a dominating set of size at most {$ k' $}, (2) {$H$} has {$ O((j + 1)^{i + 1} k^{i^2}) $} vertices, and (3) {$ k' = O((j + 1)^{i + 1} k^{i^2}) $}. Since {$d$}-degenerate graphs do not have {$ K_{d + 1, d + 1} $} as a subgraph, this immediately yields a polynomial kernel on {$ O((d + 2)^{d + 2} {k^{(d + 1)}}^2) $} vertices for the {$k$}-Dominating Set problem on {$d$}-degenerate graphs, solving an open problem posed by Alon and Gutner [Alon and Gutner 2008; Gutner 2009]. The most general class of graphs for which a polynomial kernel was previously known for {$k$}-Dominating Set is the class of {$ K_h $}-topological-minor-free graphs [Gutner 2009]. Graphs of bounded degeneracy are the most general class of graphs for which an FPT algorithm was previously known for this problem. {$ K_h $}-topological-minor-free graphs are {$ K_{i, j} $}-free for suitable values of {$i$}, {$j$} (but not vice-versa), and so our results show that {$k$}-Dominating Set has both FPT algorithms and polynomial kernels in strictly more general classes of graphs. Using the same techniques, we also obtain an {$ O(j k^i) $} vertex-kernel for the {$k$}-Independent Dominating Set problem on {$ K_{i, j} $}-free graphs.", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bodlaender:2012:EAT, author = "Hans L. Bodlaender and Fedor V. Fomin and Arie M. C. A. Koster and Dieter Kratsch and Dimitrios M. Thilikos", title = "On exact algorithms for treewidth", journal = j-TALG, volume = "9", number = "1", pages = "12:1--12:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390188", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give experimental and theoretical results on the problem of computing the treewidth of a graph by exact exponential-time algorithms using exponential space or using only polynomial space. We first report on an implementation of a dynamic programming algorithm for computing the treewidth of a graph with running time O *(2 $^n$). This algorithm is based on the old dynamic programming method introduced by Held and Karp for the Traveling Salesman problem. We use some optimizations that do not affect the worst case running time but improve on the running time on actual instances and can be seen to be practical for small instances. We also consider the problem of computing Treewidth under the restriction that the space used is only polynomial and give a simple O *(4 $^n$) algorithm that requires polynomial space. We also show that with a more complicated algorithm using balanced separators, Treewidth can be computed in O *(2.9512 $^n$) time and polynomial space.", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Amir:2012:CDC, author = "Amihood Amir and Estrella Eisenberg and Avivit Levy and Ely Porat and Natalie Shapira", title = "Cycle detection and correction", journal = j-TALG, volume = "9", number = "1", pages = "13:1--13:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390189", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Assume that a natural cyclic phenomenon has been measured, but the data is corrupted by errors. The type of corruption is application-dependent and may be caused by measurements errors, or natural features of the phenomenon. We assume that an appropriate metric exists, which measures the amount of corruption experienced. This article studies the problem of recovering the correct cycle from data corrupted by various error models, formally defined as the period recovery problem. Specifically, we define a metric property which we call pseudolocality and study the period recovery problem under pseudolocal metrics. Examples of pseudolocal metrics are the Hamming distance, the swap distance, and the interchange (or Cayley) distance. We show that for pseudolocal metrics, periodicity is a powerful property allowing detecting the original cycle and correcting the data, under suitable conditions. Some surprising features of our algorithm are that we can efficiently identify the period in the corrupted data, up to a number of possibilities logarithmic in the length of the data string, even for metrics whose calculation is NP-hard. For the Hamming metric, we can reconstruct the corrupted data in near-linear time even for unbounded alphabets. This result is achieved using the property of separation in the self-convolution vector and Reed--Solomon codes. Finally, we employ our techniques beyond the scope of pseudo-local metrics and give a recovery algorithm for the non-pseudolocal Levenshtein edit metric.", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Weimann:2013:RPD, author = "Oren Weimann and Raphael Yuster", title = "Replacement Paths and Distance Sensitivity Oracles via Fast Matrix Multiplication", journal = j-TALG, volume = "9", number = "2", pages = "14:1--14:??", month = mar, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2438645.2438646", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:37 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A distance sensitivity oracle of an $n$-vertex graph {$ G = (V, E) $} is a data structure that can report shortest paths when edges of the graph fail. A query ({$ u \in V $}, {$ v \in V $}, {$ S \subseteq E $}) to this oracle returns a shortest $u$-to-$v$ path in the graph {$ G' = (V, E \backslash S) $}. We present randomized (Monte Carlo) algorithms for constructing a distance sensitivity oracle of size {$ \tilde {O}(n^{3 - \alpha }) $} for {$ | S | = O(\lg n / \lg \lg n) $} and any choice of $ 0 < \alpha < 1 $. For real edge-lengths, the oracle is constructed in {$ O(n^{4 - \alpha }) $} time and a query to this oracle takes {$ \tilde {O} (n^{2 - 2(1 - \alpha) / |S|}) $} time. For integral edge-lengths in {$ \{ - M, \ldots {}, M \} $}, using the current $ \omega < 2.376 $ matrix multiplication exponent, the oracle is constructed in {$ O(M n^{3.376 - \alpha }) $} time with {$ \tilde {O}({n^{2 - (1 - \alpha) / |S|}}) $} query, or alternatively in {$ O(M^{0.681} n^{3.575 - \alpha }) $} time with {$ \tilde {O}(n^{2 - 2(1 - \alpha) / |S|}) $} query. Distance sensitivity oracles generalize the replacement paths problem in which $u$ and $v$ are known in advance and {$ | S | = 1 $}. In other words, if {$P$} is a shortest path from $u$ to $v$ in {$G$}, then the replacement paths problem asks to compute, for every edge $e$ on {$P$}, a shortest $u$-to-$v$ path that avoids $e$. Our new technique for constructing distance sensitivity oracles using fast matrix multiplication also yields the first subcubic-time algorithm for the replacement paths problem when the edge-lengths are small integers. In particular, it yields a randomized (Monte Carlo) {$ \tilde {O}(M n^{2.376} + M^{2 / 3} n^{2.584}) $}-time algorithm for the replacement paths problem assuming {$ M \leq n^{0.624} $}. Finally, we mention that both our replacement paths algorithm and our distance sensitivity oracle can be made to work, in the same time and space bounds, for the case of failed vertices rather than edges, that is, when {$S$} is a set of vertices and we seek a shortest $u$-to-$v$ path in the graph obtained from {$G$} by removing all vertices in {$S$} and their adjacent edges.", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Roditty:2013:AG, author = "Liam Roditty and Roei Tov", title = "Approximating the Girth", journal = j-TALG, volume = "9", number = "2", pages = "15:1--15:??", month = mar, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2438645.2438647", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:37 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article considers the problem of computing a minimum weight cycle in weighted undirected graphs. Given a weighted undirected graph {$ G = (V, E, w) $}, let {$C$} be a minimum weight cycle of G, let w (C) be the weight of {$C$}, and let {$ w_{\rm max}(C) $} be the weight of the maximum edge of {$C$}. We obtain three new approximation algorithms for the minimum weight cycle problem: (1) for integral weights from the range {$ [1, M] $}, an algorithm that reports a cycle of weight at most {$ 4 / 3 w (C) $} in {$ O(n^2 \log n (\log n + \log M)) $} time; (2) For integral weights from the range {$ [1, M] $}, an algorithm that reports a cycle of weight at most {$ w(C) + w_{\rm max}(C) $} in {$ O(n^2 \log n (\log n + \log M)) $} time; (3) For nonnegative real edge weights, an algorithm that for any $ \epsilon > 0 $ reports a cycle of weight at most {$ (4 / 3 + \epsilon) w(C) $} in {$ O(1 \epsilon n^2 \log n (\log \log n)) $} time. In a recent breakthrough, Williams and Williams [2010] showed that a subcubic algorithm, that computes the exact minimum weight cycle in undirected graphs with integral weights from the range {$ [1, M] $}, implies a subcubic algorithm for computing all-pairs shortest paths in directed graphs with integral weights from the range {$ [ - M, M] $}. This implies that in order to get a subcubic algorithm for computing a minimum weight cycle, we have to relax the problem and to consider an approximated solution. Lingas and Lundell [2009] were the first to consider approximation in the context of minimum weight cycle in weighted graphs. They presented a 2-approximation algorithm for integral weights with {$ O(n^2 \log n (\log n + \log M)) $} running time. They also posed, as an open problem, the question whether it is possible to obtain a subcubic algorithm with a $c$ approximation, where $ c < 2 $. The current article answers this question in the affirmative, by presenting an algorithm with 4/3-approximation and the same running time. Surprisingly, the approximation factor of 4/3 is not accidental. We show, using the new result of Williams and Williams [2010], that a subcubic combinatorial algorithm with $ (4 / 3 - \epsilon) $-approximation, where $ 0 < \epsilon \leq 1 / 3 $, implies a subcubic combinatorial algorithm for multiplying two boolean matrices.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Kawarabayashi:2013:LAA, author = "Ken-Ichi Kawarabayashi and Yusuke Kobayashi", title = "An {$ O(\log n) $}-Approximation Algorithm for the Edge-Disjoint Paths Problem in {Eulerian} Planar Graphs", journal = j-TALG, volume = "9", number = "2", pages = "16:1--16:??", month = mar, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2438645.2438648", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:37 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we study an approximation algorithm for the maximum edge-disjoint paths problem. In this problem, we are given a graph and a collection of pairs of vertices, and the objective is to find the maximum number of pairs that can be connected by edge-disjoint paths. We give an {$ O(\log n) $}-approximation algorithm for the maximum edge-disjoint paths problem when an input graph is either 4-edge-connected planar or Eulerian planar. This improves an {$ O(\log^2 n) $}-approximation algorithm given by Kleinberg [2005] for Eulerian planar graphs. Our result also generalizes the result by Chekuri et al. [2004, 2005] who gave an {$ O(\log n) $}-approximation algorithm for the maximum edge-disjoint paths problem with congestion two when an input graph is planar.", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Fraigniaud:2013:DIE, author = "Pierre Fraigniaud and Andrzej Pelc", title = "Delays Induce an Exponential Memory Gap for Rendezvous in Trees", journal = j-TALG, volume = "9", number = "2", pages = "17:1--17:??", month = mar, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2438645.2438649", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:37 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The aim of rendezvous in a graph is meeting of two mobile agents at some node of an unknown anonymous connected graph. In this article, we focus on rendezvous in trees, and, analogously to the efforts that have been made for solving the exploration problem with compact automata, we study the size of memory of mobile agents that permits to solve the rendezvous problem deterministically. We assume that the agents are identical, and move in synchronous rounds. We first show that if the delay between the starting times of the agents is arbitrary, then the lower bound on memory required for rendezvous is {$ \Omega (\log n) $} bits, even for the line of length n. This lower bound meets a previously known upper bound of {$ O(\log n) $} bits for rendezvous in arbitrary graphs of size at most $n$. Our main result is a proof that the amount of memory needed for rendezvous with simultaneous start depends essentially on the number $l$ of leaves of the tree, and is exponentially less impacted by the number $n$ of nodes. Indeed, we present two identical agents with {$ O(\log l + \log \log n) $} bits of memory that solve the rendezvous problem in all trees with at most $n$ nodes and at most $l$ leaves. Hence, for the class of trees with polylogarithmically many leaves, there is an exponential gap in minimum memory size needed for rendezvous between the scenario with arbitrary delay and the scenario with delay zero. Moreover, we show that our upper bound is optimal by proving that {$ \Omega (\log l + \log \log n) $} bits of memory are required for rendezvous, even in the class of trees with degrees bounded by 3.", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bansal:2013:SSA, author = "Nikhil Bansal and Ho-Leung Chan and Kirk Pruhs", title = "Speed Scaling with an Arbitrary Power Function", journal = j-TALG, volume = "9", number = "2", pages = "18:1--18:??", month = mar, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2438645.2438650", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:37 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article initiates a theoretical investigation into online scheduling problems with speed scaling where the allowable speeds may be discrete, and the power function may be arbitrary, and develops algorithmic analysis techniques for this setting. We show that a natural algorithm, which uses Shortest Remaining Processing Time for scheduling and sets the power to be one more than the number of unfinished jobs, is 3-competitive for the objective of total flow time plus energy. We also show that another natural algorithm, which uses Highest Density First for scheduling and sets the power to be the fractional weight of the unfinished jobs, is a 2-competitive algorithm for the objective of fractional weighted flow time plus energy.", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hochbaum:2013:AAM, author = "Dorit S. Hochbaum and Asaf Levin", title = "Approximation Algorithms for a Minimization Variant of the Order-Preserving Submatrices and for Biclustering Problems", journal = j-TALG, volume = "9", number = "2", pages = "19:1--19:??", month = mar, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2438645.2438651", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:37 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Finding a largest Order-Preserving SubMatrix, OPSM, is an important problem arising in the discovery of patterns in gene expression. Ben-Dor et al. formulated the problem in Ben-Dor et al. [2003]. They further showed that the problem is NP-complete and provided a greedy heuristic for the problem. The complement of the OPSM problem, called MinOPSM, is to delete the least number of entries in the matrix so that the remaining submatrix is order preserving. We devise a 5-approximation algorithm for the MinOPSM based on a formulation of the problem as a quadratic, nonseparable set cover problem. An alternative formulation combined with a primal-dual algorithm improves the approximation factor to 3. The complexity of both algorithms for a matrix of size $ m \times n $ is {$ O(m^2 n) $}. We further comment on the related biclustering problem.", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chawla:2013:FSI, author = "Shuchi Chawla and Prasad Raghavendra and Dana Randall", title = "Foreword to the {Special Issue on SODA'11}", journal = j-TALG, volume = "9", number = "3", pages = "20:1--20:??", month = jun, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2483699.2483700", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:46 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ailon:2013:AOU, author = "Nir Ailon and Edo Liberty", title = "An Almost Optimal Unrestricted Fast {Johnson--Lindenstrauss Transform}", journal = j-TALG, volume = "9", number = "3", pages = "21:1--21:??", month = jun, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2483699.2483701", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:46 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The problems of random projections and sparse reconstruction have much in common and individually received much attention. Surprisingly, until now they progressed in parallel and remained mostly separate. Here, we employ new tools from probability in Banach spaces that were successfully used in the context of sparse reconstruction to advance on an open problem in random projection. In particular, we generalize and use an intricate result by Rudelson and Veshynin [2008] for sparse reconstruction which uses Dudley's theorem for bounding Gaussian processes. Our main result states that any set of {$ N = \exp (\tilde {O}(n)) $} real vectors in $n$-dimensional space can be linearly mapped to a space of dimension {$ k = O(\log N \polylog (n)) $}, while (1) preserving the pairwise distances among the vectors to within any constant distortion and (2) being able to apply the transformation in time {$ O(n \log n) $} on each vector. This improves on the best known bound {$ N = \exp (\tilde {O}(n^{1 / 2})) $} achieved by Ailon and Liberty [2009] and {$ N = e x p(\tilde {O}(n^{1 / 3})) $} by Ailon and Chazelle [2010]. The dependence in the distortion constant however is suboptimal, and since the publication of an early version of the work, the gap between upper and lower bounds has been considerably tightened obtained by Krahmer and Ward [2011]. For constant distortion, this settles the open question posed by these authors up to a $ \polylog (n) $ factor while considerably simplifying their constructions.", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chan:2013:PPS, author = "Timothy M. Chan", title = "Persistent Predecessor Search and Orthogonal Point Location on the Word {RAM}", journal = j-TALG, volume = "9", number = "3", pages = "22:1--22:??", month = jun, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2483699.2483702", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:46 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We answer a basic data structuring question (e.g., raised by Dietz and Raman [1991]): Can van Emde Boas trees be made persistent, without changing their asymptotic query/update time? We present a (partially) persistent data structure that supports predecessor search in a set of integers in {$ \{ 1, \ldots {}, U \} $} under an arbitrary sequence of n insertions and deletions, with {$ O(\log \log U) $} expected query time and expected amortized update time, and {$ O(n) $} space. The query bound is optimal in {$U$} for linear-space structures and improves previous near-{$ O((\log \log U)^2) $} methods. The same method solves a fundamental problem from computational geometry: point location in orthogonal planar subdivisions (where edges are vertical or horizontal). We obtain the first static data structure achieving {$ O(\log \log U) $} worst-case query time and linear space. This result is again optimal in {$U$} for linear-space structures and improves the previous {$ O((\log \log U)^2) $} method by de Berg et al. [1995]. The same result also holds for higher-dimensional subdivisions that are orthogonal binary space partitions, and for certain nonorthogonal planar subdivisions such as triangulations without small angles. Many geometric applications follow, including improved query times for orthogonal range reporting for dimensions $ \geq 3 $ on the RAM. Our key technique is an interesting new van-Emde-Boas--style recursion that alternates between two strategies, both quite simple.", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Daskalakis:2013:CAN, author = "Constantinos Daskalakis", title = "On the Complexity of Approximating a {Nash} Equilibrium", journal = j-TALG, volume = "9", number = "3", pages = "23:1--23:??", month = jun, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2483699.2483703", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:46 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show that computing a relatively (i.e., multiplicatively as opposed to additively) approximate Nash equilibrium in two-player games is PPAD-complete, even for constant values of the approximation. Our result is the first constant inapproximability result for Nash equilibrium, since the original results on the computational complexity of the problem [Daskalakis et al. 2006a; Chen and Deng 2006]. Moreover, it provides an apparent---assuming that PPAD is not contained in TIME({$ n^{O(\log n)} $})---dichotomy between the complexities of additive and relative approximations, as for constant values of additive approximation a quasi-polynomial-time algorithm is known [Lipton et al. 2003]. Such a dichotomy does not exist for values of the approximation that scale inverse-polynomially with the size of the game, where both relative and additive approximations are PPAD-complete [Chen et al. 2006]. As a byproduct, our proof shows that (unconditionally) the sparse-support lemma [Lipton et al. 2003] cannot be extended to relative notions of constant approximation.", acknowledgement = ack-nhfb, articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Eisenbrand:2013:PDP, author = "Friedrich Eisenbrand and D{\"o}m{\"o}t{\"o}r P{\'a}lv{\"o}lgyi and Thomas Rothvo{\ss}", title = "Bin Packing via Discrepancy of Permutations", journal = j-TALG, volume = "9", number = "3", pages = "24:1--24:??", month = jun, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2483699.2483704", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:46 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A well-studied special case of bin packing is the 3-partition problem, where n items of size > 1/4 have to be packed in a minimum number of bins of capacity one. The famous Karmarkar-Karp algorithm transforms a fractional solution of a suitable LP relaxation for this problem into an integral solution that requires at most {$ O(\log n) $} additional bins. The three-permutations-problem of Beck is the following. Given any three permutations on n symbols, color the symbols red and blue, such that in any interval of any of those permutations, the number of red and blue symbols is roughly the same. The necessary difference is called the discrepancy. We establish a surprising connection between bin packing and Beck's problem: The additive integrality gap of the 3-partition linear programming relaxation can be bounded by the discrepancy of three permutations. This connection yields an alternative method to establish an {$ O(\log n) $} bound on the additive integrality gap of the 3-partition. Conversely, making use of a recent example of three permutations, for which a discrepancy of {$ \Omega (\log n) $} is necessary, we prove the following: The {$ O(\log^2 n) $} upper bound on the additive gap for bin packing with arbitrary item sizes cannot be improved by any technique that is based on rounding up items. This lower bound holds for a large class of algorithms including the Karmarkar-Karp procedure.", acknowledgement = ack-nhfb, articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gawrychowski:2013:OPM, author = "Pawel Gawrychowski", title = "Optimal Pattern Matching in {LZW} Compressed Strings", journal = j-TALG, volume = "9", number = "3", pages