%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "1.09", %%% date = "14 October 2017", %%% time = "10:26:08 MDT", %%% filename = "stoc2010.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 = "http://www.math.utah.edu/~beebe", %%% checksum = "31388 10295 60046 545326", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "ACM Symposium on Theory of Computing (STOC)", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a COMPLETE bibliography of %%% publications in the ACM Symposium on Theory %%% of Computing (STOC) conference proceedings %%% for the decade 2010--2019. Companion %%% bibliographies stoc19xx.bib and stoc20xx.bib %%% cover other decades, and stoc.bib contains %%% entries for just the proceedings volumes %%% themselves. %%% %%% There is World-Wide Web sites for these %%% publications at %%% %%% http://dl.acm.org/event.cfm?id=RE224 %%% http://www.sigact.org/stoc.html?searchterm=STOC %%% http://www.acm.org/pubs/contents/proceedings/series/stoc/ %%% %%% At version 1.09, the year coverage looked %%% like this: %%% %%% 2006 ( 2) 2009 ( 0) 2012 ( 90) %%% 2007 ( 0) 2010 ( 83) 2013 ( 101) %%% 2008 ( 0) 2011 ( 85) %%% %%% InProceedings: 356 %%% Proceedings: 5 %%% %%% Total entries: 361 %%% %%% 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|http://www.math.utah.edu/~beebe/|"}

%%% ==================================================================== %%% Publisher abbreviations:

@String{pub-ACM= "ACM Press"} @String{pub-ACM:adr= "New York, NY, USA"}

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

@InProceedings{Akavia:2006:BOW, author = "Adi Akavia and Oded Goldreich and Shafi Goldwasser and Dana Moshkovitz", title = "On basing one-way functions on {NP}-hardness", crossref = "ACM:2006:SPT", pages = "701--710", year = "2006", bibdate = "Thu May 25 06:19:54 MDT 2006", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", note = "See erratum \cite{Akavia:2010:EBO}.", acknowledgement = ack-nhfb, } @InProceedings{Kannan:2010:SMM, author = "Ravindran Kannan", title = "Spectral methods for matrices and tensors", crossref = "ACM:2010:SPA", pages = "1--12", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Talagrand:2010:MSS, author = "Michel Talagrand", title = "Are many small sets explicitly small?", crossref = "ACM:2010:SPA", pages = "13--36", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Montanari:2010:MPA, author = "Andrea Montanari", title = "Message passing algorithms: a success looking for theoreticians", crossref = "ACM:2010:SPA", pages = "37--38", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Goel:2010:PML, author = "Ashish Goel and Michael Kapralov and Sanjeev Khanna", title = "Perfect matchings in $o(n \log n)$ time in regular bipartite graphs", crossref = "ACM:2010:SPA", pages = "39--46", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Leighton:2010:ELV, author = "F. Thomson Leighton and Ankur Moitra", title = "Extensions and limits to vertex sparsification", crossref = "ACM:2010:SPA", pages = "47--56", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Kolla:2010:SSN, author = "Alexandra Kolla and Yury Makarychev and Amin Saberi and Shang-Hua Teng", title = "Subgraph sparsification and nearly optimal ultrasparsifiers", crossref = "ACM:2010:SPA", pages = "57--66", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Barak:2010:HCI, author = "Boaz Barak and Mark Braverman and Xi Chen and Anup Rao", title = "How to compress interactive communication", crossref = "ACM:2010:SPA", pages = "67--76", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Klauck:2010:SDP, author = "Hartmut Klauck", title = "A strong direct product theorem for disjointness", crossref = "ACM:2010:SPA", pages = "77--86", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Beame:2010:HAP, author = "Paul Beame and Trinh Huynh and Toniann Pitassi", title = "Hardness amplification in proof complexity", crossref = "ACM:2010:SPA", pages = "87--96", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Gao:2010:LBO, author = "Pu Gao and Nicholas C. Wormald", title = "Load balancing and orientability thresholds for random hypergraphs", crossref = "ACM:2010:SPA", pages = "97--104", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Bayati:2010:CAI, author = "Mohsen Bayati and David Gamarnik and Prasad Tetali", title = "Combinatorial approach to the interpolation method and scaling limits in sparse random graphs", crossref = "ACM:2010:SPA", pages = "105--114", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Hirai:2010:MMP, author = "Hiroshi Hirai", title = "The maximum multiflow problems with bounded fractionality", crossref = "ACM:2010:SPA", pages = "115--120", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Madry:2010:FAS, author = "Aleksander Madry", title = "Faster approximation schemes for fractional multicommodity flow problems via dynamic graph algorithms", crossref = "ACM:2010:SPA", pages = "121--130", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Aaronson:2010:FCQ, author = "Scott Aaronson and Andrew Drucker", title = "A full characterization of quantum advice", crossref = "ACM:2010:SPA", pages = "131--140", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Aaronson:2010:BPH, author = "Scott Aaronson", title = "{BQP} and the polynomial hierarchy", crossref = "ACM:2010:SPA", pages = "141--150", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Ambainis:2010:QLL, author = "Andris Ambainis and Julia Kempe and Or Sattath", title = "A quantum {Lov{\'a}sz} local lemma", crossref = "ACM:2010:SPA", pages = "151--160", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{De:2010:NOE, author = "Anindya De and Thomas Vidick", title = "Near-optimal extractors against quantum storage", crossref = "ACM:2010:SPA", pages = "161--170", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Applebaum:2010:PKC, author = "Benny Applebaum and Boaz Barak and Avi Wigderson", title = "Public-key cryptography from different assumptions", crossref = "ACM:2010:SPA", pages = "171--180", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Ajtai:2010:ORC, author = "Mikl{\'o}s Ajtai", title = "Oblivious {RAM}s without cryptographic assumptions", crossref = "ACM:2010:SPA", pages = "181--190", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Goyal:2010:RCC, author = "Vipul Goyal and Abhishek Jain", title = "On the round complexity of covert computation", crossref = "ACM:2010:SPA", pages = "191--200", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Bhaskara:2010:DHL, author = "Aditya Bhaskara and Moses Charikar and Eden Chlamtac and Uriel Feige and Aravindan Vijayaraghavan", title = "Detecting high log-densities: an {$O(n^{1/4})$} approximation for densest $k$-subgraph", crossref = "ACM:2010:SPA", pages = "201--210", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Bateni:2010:ASS, author = "MohammadHossein Bateni and MohammadTaghi Hajiaghayi and D{\'a}niel Marx", title = "Approximation schemes for {Steiner} forest on planar graphs and graphs of bounded treewidth", crossref = "ACM:2010:SPA", pages = "211--220", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Dey:2010:OHC, author = "Tamal K. Dey and Anil N. Hirani and Bala Krishnamoorthy", title = "Optimal homologous cycles, total unimodularity, and linear programming", crossref = "ACM:2010:SPA", pages = "221--230", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Williams:2010:IES, author = "Ryan Williams", title = "Improving exhaustive search implies superpolynomial lower bounds", crossref = "ACM:2010:SPA", pages = "231--240", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Paturi:2010:CCS, author = "Ramamohan Paturi and Pavel Pudlak", title = "On the complexity of circuit satisfiability", crossref = "ACM:2010:SPA", pages = "241--250", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Dell:2010:SAN, author = "Holger Dell and Dieter van Melkebeek", title = "Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses", crossref = "ACM:2010:SPA", pages = "251--260", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Magniez:2010:RWP, author = "Fr{\'e}d{\'e}ric Magniez and Claire Mathieu and Ashwin Nayak", title = "Recognizing well-parenthesized expressions in the streaming model", crossref = "ACM:2010:SPA", pages = "261--270", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Braverman:2010:MID, author = "Vladimir Braverman and Rafail Ostrovsky", title = "Measuring independence of datasets", crossref = "ACM:2010:SPA", pages = "271--280", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Braverman:2010:ZOF, author = "Vladimir Braverman and Rafail Ostrovsky", title = "Zero-one frequency laws", crossref = "ACM:2010:SPA", pages = "281--290", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Orlin:2010:IAC, author = "James B. Orlin", title = "Improved algorithms for computing {Fisher}'s market clearing prices", crossref = "ACM:2010:SPA", pages = "291--300", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Hartline:2010:BAM, author = "Jason D. Hartline and Brendan Lucier", title = "{Bayesian} algorithmic mechanism design", crossref = "ACM:2010:SPA", pages = "301--310", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Chawla:2010:MPM, author = "Shuchi Chawla and Jason D. Hartline and David L. Malec and Balasubramanian Sivan", title = "Multi-parameter mechanism design and sequential posted pricing", crossref = "ACM:2010:SPA", pages = "311--320", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Lokshtanov:2010:SSA, author = "Daniel Lokshtanov and Jesper Nederlof", title = "Saving space by algebraization", crossref = "ACM:2010:SPA", pages = "321--330", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Haramaty:2010:SCQ, author = "Elad Haramaty and Amir Shpilka", title = "On the structure of cubic and quartic polynomials", crossref = "ACM:2010:SPA", pages = "331--340", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Dasgupta:2010:SJL, author = "Anirban Dasgupta and Ravi Kumar and Tam{\'a}s Sarlos", title = "A sparse {Johnson--Lindenstrauss} transform", crossref = "ACM:2010:SPA", pages = "341--350", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Micciancio:2010:DSE, author = "Daniele Micciancio and Panagiotis Voulgaris", title = "A deterministic single exponential time algorithm for most lattice problems based on {Voronoi} cell computations", crossref = "ACM:2010:SPA", pages = "351--358", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Cardinal:2010:SUP, author = "Jean Cardinal and Samuel Fiorini and Gwena{\"e}l Joret and Rapha{\"e}l M. Jungers and J. Ian Munro", title = "Sorting under partial information (without the ellipsoid algorithm)", crossref = "ACM:2010:SPA", pages = "359--368", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Lee:2010:MMP, author = "Jon Lee and Maxim Sviridenko and Jan Vondrak", title = "Matroid matching: the power of local search", crossref = "ACM:2010:SPA", pages = "369--378", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Bhattacharya:2010:BCA, author = "Sayan Bhattacharya and Gagan Goel and Sreenivas Gollapudi and Kamesh Munagala", title = "Budget constrained auctions with heterogeneous items", crossref = "ACM:2010:SPA", pages = "379--388", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Fraigniaud:2010:SSW, author = "Pierre Fraigniaud and George Giakkoupis", title = "On the searchability of small-world networks with arbitrary underlying structure", crossref = "ACM:2010:SPA", pages = "389--398", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Chierichetti:2010:ATB, author = "Flavio Chierichetti and Silvio Lattanzi and Alessandro Panconesi", title = "Almost tight bounds for rumour spreading with conductance", crossref = "ACM:2010:SPA", pages = "399--408", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Guruswami:2010:LDR, author = "Venkatesan Guruswami and Johan H{\aa}stad and Swastik Kopparty", title = "On the list-decodability of random linear codes", crossref = "ACM:2010:SPA", pages = "409--416", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Kopparty:2010:LLD, author = "Swastik Kopparty and Shubhangi Saraf", title = "Local list-decoding and testing of random linear codes from high error", crossref = "ACM:2010:SPA", pages = "417--426", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Meka:2010:PGP, author = "Raghu Meka and David Zuckerman", title = "Pseudorandom generators for polynomial threshold functions", crossref = "ACM:2010:SPA", pages = "427--436", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Haitner:2010:EIC, author = "Iftach Haitner and Omer Reingold and Salil Vadhan", title = "Efficiency improvements in constructing pseudorandom generators from one-way functions", crossref = "ACM:2010:SPA", pages = "437--446", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Verbin:2010:LBT, author = "Elad Verbin and Qin Zhang", title = "The limits of buffering: a tight lower bound for dynamic membership in the external memory model", crossref = "ACM:2010:SPA", pages = "447--456", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Onak:2010:MLM, author = "Krzysztof Onak and Ronitt Rubinfeld", title = "Maintaining a large matching and a small vertex cover", crossref = "ACM:2010:SPA", pages = "457--464", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Duan:2010:COF, author = "Ran Duan and Seth Pettie", title = "Connectivity oracles for failure prone graphs", crossref = "ACM:2010:SPA", pages = "465--474", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Gilbert:2010:ASR, author = "Anna C. Gilbert and Yi Li and Ely Porat and Martin J. Strauss", title = "Approximate sparse recovery: optimizing time and measurements", crossref = "ACM:2010:SPA", pages = "475--484", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Godoy:2010:HPD, author = "Guillem Godoy and Omer Gim{\'e}nez and Lander Ramos and Carme {\`A}lvarez", title = "The {HOM} problem is decidable", crossref = "ACM:2010:SPA", pages = "485--494", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Kawamura:2010:CTO, author = "Akitoshi Kawamura and Stephen Cook", title = "Complexity theory for operators in analysis", crossref = "ACM:2010:SPA", pages = "495--502", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Burgisser:2010:SPE, author = "Peter B{\"u}rgisser and Felipe Cucker", title = "Solving polynomial equations in smoothed polynomial time and a near solution to {Smale}'s 17th problem", crossref = "ACM:2010:SPA", pages = "503--512", year = "2010", DOI = "https://doi.org/10.1145/1806689.1806759", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "The 17th of the problems proposed by Steve Smale for the 21st century asks for the existence of a deterministic algorithm computing an approximate solution of a system of $n$ complex polynomials in $n$ unknowns in time polynomial, on the average, in the size $N$ of the input system. A partial solution to this problem was given by Carlos Beltran and Luis Miguel Pardo who exhibited a randomized algorithm, call it LV, doing so. In this paper we further extend this result in several directions. Firstly, we perform a smoothed analysis (in the sense of Spielman and Teng) of algorithm LV and prove that its smoothed complexity is polynomial in the input size and $\sigma - 1$, where $\sigma$ controls the size of the random perturbation of the input systems. Secondly, we perform a condition-based analysis of LV. That is, we give a bound, for each system $f$, of the expected running time of LV with input $f$. In addition to its dependence on $N$ this bound also depends on the condition of $f$. Thirdly, and to conclude, we return to Smale's 17th problem as originally formulated for deterministic algorithms. We exhibit such an algorithm and show that its average complexity is $N^{O(\log \log N)}$. This is nearly a solution to Smale's 17th problem.", acknowledgement = ack-nhfb, } @InProceedings{Kuhn:2010:DCD, author = "Fabian Kuhn and Nancy Lynch and Rotem Oshman", title = "Distributed computation in dynamic networks", crossref = "ACM:2010:SPA", pages = "513--522", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Sherstov:2010:OBS, author = "Alexander A. Sherstov", title = "Optimal bounds for sign-representing the intersection of two halfspaces by polynomials", crossref = "ACM:2010:SPA", pages = "523--532", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Diakonikolas:2010:BAS, author = "Ilias Diakonikolas and Prahladh Harsha and Adam Klivans and Raghu Meka and Prasad Raghavendra and Rocco A. Servedio and Li-Yang Tan", title = "Bounding the average sensitivity and noise sensitivity of polynomial threshold functions", crossref = "ACM:2010:SPA", pages = "533--542", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Harsha:2010:IPP, author = "Prahladh Harsha and Adam Klivans and Raghu Meka", title = "An invariance principle for polytopes", crossref = "ACM:2010:SPA", pages = "543--552", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Kalai:2010:ELM, author = "Adam Tauman Kalai and Ankur Moitra and Gregory Valiant", title = "Efficiently learning mixtures of two {Gaussians}", crossref = "ACM:2010:SPA", pages = "553--562", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{VAgh:2010:AUN, author = "L{\'a}szl{\'o} A. V{\'e}gh", title = "Augmenting undirected node-connectivity by one", crossref = "ACM:2010:SPA", pages = "563--572", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Jain:2010:QP, author = "Rahul Jain and Zhengfeng Ji and Sarvagya Upadhyay and John Watrous", title = "{QIP $=$ PSPACE}", crossref = "ACM:2010:SPA", pages = "573--582", year = "2010", DOI = "https://doi.org/10.1145/1806689.1806768", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We prove that the complexity class QIP, which consists of all problems having quantum interactive proof systems, is contained in PSPACE. This containment is proved by applying a parallelized form of the matrix multiplicative weights update method to a class of semidefinite programs that captures the computational power of quantum interactive proofs. As the containment of PSPACE in QIP follows immediately from the well-known equality IP $=$ PSPACE, the equality QIP $=$ PSPACE follows.", acknowledgement = ack-nhfb, remark = "This work won the conference's Best Paper Award. An updated version appears in Comm. ACM 53(12) 102--109 (December 2010), \url{https://doi.org/10.1145/1859204.1859231}.", } @InProceedings{Byrka:2010:ILB, author = "Jaroslaw Byrka and Fabrizio Grandoni and Thomas Rothvo{\ss} and Laura Sanit{\`a}", title = "An improved {LP}-based approximation for {Steiner} tree", crossref = "ACM:2010:SPA", pages = "583--592", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Dodis:2010:CBL, author = "Yevgeniy Dodis and Mihai Patrascu and Mikkel Thorup", title = "Changing base without losing space", crossref = "ACM:2010:SPA", pages = "593--602", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Patrascu:2010:TPL, author = "Mihai Patrascu", title = "Towards polynomial lower bounds for dynamic problems", crossref = "ACM:2010:SPA", pages = "603--610", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Fraigniaud:2010:OAS, author = "Pierre Fraigniaud and Amos Korman", title = "An optimal ancestry scheme and small universal posets", crossref = "ACM:2010:SPA", pages = "611--620", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Lee:2010:BSM, author = "James R. Lee and Mohammad Moharrami", title = "Bilipschitz snowflakes and metrics of negative type", crossref = "ACM:2010:SPA", pages = "621--630", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Raghavendra:2010:AIS, author = "Prasad Raghavendra and David Steurer and Prasad Tetali", title = "Approximations for the isoperimetric and spectral profile of graphs and related parameters", crossref = "ACM:2010:SPA", pages = "631--640", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Varadarajan:2010:WGS, author = "Kasturi Varadarajan", title = "Weighted geometric set cover via quasi-uniform sampling", crossref = "ACM:2010:SPA", pages = "641--648", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Karnin:2010:DIT, author = "Zohar S. Karnin and Partha Mukhopadhyay and Amir Shpilka and Ilya Volkovich", title = "Deterministic identity testing of depth-4 multilinear circuits with bounded top fan-in", crossref = "ACM:2010:SPA", pages = "649--658", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Raz:2010:TRL, author = "Ran Raz", title = "Tensor-rank and lower bounds for arithmetic formulas", crossref = "ACM:2010:SPA", pages = "659--666", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{HrubeAa:2010:NCC, author = "Pavel Hrube and Avi Wigderson and Amir Yehudayoff", title = "Non-commutative circuits and the sum-of-squares problem", crossref = "ACM:2010:SPA", pages = "667--676", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Arvind:2010:HND, author = "Vikraman Arvind and Srikanth Srinivasan", title = "On the hardness of the noncommutative determinant", crossref = "ACM:2010:SPA", pages = "677--686", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Kawarabayashi:2010:SPG, author = "Ken-ichi Kawarabayashi and Paul Wollan", title = "A shorter proof of the graph minor algorithm: the unique linkage theorem", crossref = "ACM:2010:SPA", pages = "687--694", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Kawarabayashi:2010:OCP, author = "Ken-ichi Kawarabayashi and Bruce Reed", title = "Odd cycle packing", crossref = "ACM:2010:SPA", pages = "695--704", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Hardt:2010:GDP, author = "Moritz Hardt and Kunal Talwar", title = "On the geometry of differential privacy", crossref = "ACM:2010:SPA", pages = "705--714", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Dwork:2010:DPU, author = "Cynthia Dwork and Moni Naor and Toniann Pitassi and Guy N. Rothblum", title = "Differential privacy under continual observation", crossref = "ACM:2010:SPA", pages = "715--724", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Dyer:2010:CC, author = "Martin E. Dyer and David M. Richerby", title = "On the complexity of {\#CSP}", crossref = "ACM:2010:SPA", pages = "725--734", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Marx:2010:THP, author = "D{\'a}niel Marx", title = "Tractable hypergraph properties for constraint satisfaction and conjunctive queries", crossref = "ACM:2010:SPA", pages = "735--744", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Svensson:2010:CHP, author = "Ola Svensson", title = "Conditional hardness of precedence constrained scheduling on identical machines", crossref = "ACM:2010:SPA", pages = "745--754", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Raghavendra:2010:GEU, author = "Prasad Raghavendra and David Steurer", title = "Graph expansion and the unique games conjecture", crossref = "ACM:2010:SPA", pages = "755--764", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Roth:2010:IPM, author = "Aaron Roth and Tim Roughgarden", title = "Interactive privacy via the median mechanism", crossref = "ACM:2010:SPA", pages = "765--774", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Kasiviswanathan:2010:PPR, author = "Shiva Prasad Kasiviswanathan and Mark Rudelson and Adam Smith and Jonathan Ullman", title = "The price of privately releasing contingency tables and the spectra of random matrices with correlated rows", crossref = "ACM:2010:SPA", pages = "775--784", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Chandran:2010:PAA, author = "Nishanth Chandran and Bhavana Kanukurthi and Rafail Ostrovsky and Leonid Reyzin", title = "Privacy amplification with asymptotically optimal entropy loss", crossref = "ACM:2010:SPA", pages = "785--794", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Akavia:2010:EBO, author = "Adi Akavia and Oded Goldreich and Shafi Goldwasser and Dana Moshkovitz", title = "Erratum for: {{\em On basing one-way functions on NP-hardness}}", crossref = "ACM:2010:SPA", pages = "795--796", year = "2010", bibdate = "Wed Sep 1 10:42:57 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", note = "See \cite{Akavia:2006:BOW}.", acknowledgement = ack-nhfb, } @InProceedings{Patrascu:2011:PST, author = "Mihai Patrascu and Mikkel Thorup", title = "The power of simple tabulation hashing", crossref = "ACM:2011:SPA", pages = "1--10", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993638", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Lenzen:2011:TBP, author = "Christoph Lenzen and Roger Wattenhofer", title = "Tight bounds for parallel randomized load balancing: extended abstract", crossref = "ACM:2011:SPA", pages = "11--20", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993639", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Doerr:2011:SNS, author = "Benjamin Doerr and Mahmoud Fouz and Tobias Friedrich", title = "Social networks spread rumors in sublogarithmic time", crossref = "ACM:2011:SPA", pages = "21--30", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993640", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Regev:2011:QOW, author = "Oded Regev and Bo'az Klartag", title = "Quantum one-way communication can be exponentially stronger than classical communication", crossref = "ACM:2011:SPA", pages = "31--40", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993642", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Sherstov:2011:SDP, author = "Alexander A. Sherstov", title = "Strong direct product theorems for quantum communication and query complexity", crossref = "ACM:2011:SPA", pages = "41--50", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993643", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Chakrabarti:2011:OLB, author = "Amit Chakrabarti and Oded Regev", title = "An optimal lower bound on the communication complexity of gap-{Hamming}-distance", crossref = "ACM:2011:SPA", pages = "51--60", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993644", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Ding:2011:CTB, author = "Jian Ding and James R. Lee and Yuval Peres", title = "Cover times, blanket times, and majorizing measures", crossref = "ACM:2011:SPA", pages = "61--70", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993646", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Fung:2011:GFG, author = "Wai Shing Fung and Ramesh Hariharan and Nicholas J. A. Harvey and Debmalya Panigrahi", title = "A general framework for graph sparsification", crossref = "ACM:2011:SPA", pages = "71--80", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993647", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Kawarabayashi:2011:BAA, author = "Ken-ichi Kawarabayashi and Yusuke Kobayashi", title = "Breaking $o(n^{1/2})$-approximation algorithms for the edge-disjoint paths problem with congestion two", crossref = "ACM:2011:SPA", pages = "81--88", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993648", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Holenstein:2011:ERO, author = "Thomas Holenstein and Robin K{\"u}nzler and Stefano Tessaro", title = "The equivalence of the random oracle model and the ideal cipher model, revisited", crossref = "ACM:2011:SPA", pages = "89--98", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993650", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Gentry:2011:SSN, author = "Craig Gentry and Daniel Wichs", title = "Separating succinct non-interactive arguments from all falsifiable assumptions", crossref = "ACM:2011:SPA", pages = "99--108", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993651", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Pass:2011:LPS, author = "Rafael Pass", title = "Limits of provable security from standard assumptions", crossref = "ACM:2011:SPA", pages = "109--118", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993652", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Papadimitriou:2011:OSI, author = "Christos H. Papadimitriou and George Pierrakos", title = "On optimal single-item auctions", crossref = "ACM:2011:SPA", pages = "119--128", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993654", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Dobzinski:2011:OAC, author = "Shahar Dobzinski and Hu Fu and Robert D. Kleinberg", title = "Optimal auctions with correlated bidders are easy", crossref = "ACM:2011:SPA", pages = "129--138", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993655", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Dobzinski:2011:IRT, author = "Shahar Dobzinski", title = "An impossibility result for truthful combinatorial auctions with submodular valuations", crossref = "ACM:2011:SPA", pages = "139--148", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993656", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Dughmi:2011:COR, author = "Shaddin Dughmi and Tim Roughgarden and Qiqi Yan", title = "From convex optimization to randomized mechanisms: toward optimal combinatorial auctions", crossref = "ACM:2011:SPA", pages = "149--158", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993657", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Braverman:2011:TCM, author = "Mark Braverman and Anup Rao", title = "Towards coding for maximum errors in interactive communication", crossref = "ACM:2011:SPA", pages = "159--166", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993659", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Kopparty:2011:HRC, author = "Swastik Kopparty and Shubhangi Saraf and Sergey Yekhanin", title = "High-rate codes with sublinear-time decoding", crossref = "ACM:2011:SPA", pages = "167--176", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993660", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Zewi:2011:ATS, author = "Noga Zewi and Eli Ben-Sasson", title = "From affine to two-source extractors via approximate duality", crossref = "ACM:2011:SPA", pages = "177--186", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993661", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Hatami:2011:CTA, author = "Hamed Hatami and Shachar Lovett", title = "Correlation testing for affine invariant properties on {$\mathbb{F}_p^n$} in the high error regime", crossref = "ACM:2011:SPA", pages = "187--194", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993662", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Adsul:2011:RBG, author = "Bharat Adsul and Jugal Garg and Ruta Mehta and Milind Sohoni", title = "Rank-1 bimatrix games: a homeomorphism and a polynomial time algorithm", crossref = "ACM:2011:SPA", pages = "195--204", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993664", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Hansen:2011:EAS, author = "Kristoffer Arnsfelt Hansen and Michal Koucky and Niels Lauritzen and Peter Bro Miltersen and Elias P. Tsigaridas", title = "Exact algorithms for solving stochastic games: extended abstract", crossref = "ACM:2011:SPA", pages = "205--214", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993665", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Immorlica:2011:DA, author = "Nicole Immorlica and Adam Tauman Kalai and Brendan Lucier and Ankur Moitra and Andrew Postlewaite and Moshe Tennenholtz", title = "Dueling algorithms", crossref = "ACM:2011:SPA", pages = "215--224", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993666", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Moitra:2011:POS, author = "Ankur Moitra and Ryan O'Donnell", title = "{Pareto} optimal solutions for smoothed analysts", crossref = "ACM:2011:SPA", pages = "225--234", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993667", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Kolipaka:2011:MTM, author = "Kashyap Babu Rao Kolipaka and Mario Szegedy", title = "{Moser} and {Tardos} meet {Lov{\'a}sz}", crossref = "ACM:2011:SPA", pages = "235--244", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993669", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Moser:2011:FDS, author = "Robin A. Moser and Dominik Scheder", title = "A full derandomization of {Sch{\"o}ning}'s {$k$-SAT} algorithm", crossref = "ACM:2011:SPA", pages = "245--252", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993670", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Gopalan:2011:PGC, author = "Parikshit Gopalan and Raghu Meka and Omer Reingold and David Zuckerman", title = "Pseudorandom generators for combinatorial shapes", crossref = "ACM:2011:SPA", pages = "253--262", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993671", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Koucky:2011:PGG, author = "Michal Kouck{\'y} and Prajakta Nimbhorkar and Pavel Pudl{\'a}k", title = "Pseudorandom generators for group products: extended abstract", crossref = "ACM:2011:SPA", pages = "263--272", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993672", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Christiano:2011:EFL, author = "Paul Christiano and Jonathan A. Kelner and Aleksander Madry and Daniel A. Spielman and Shang-Hua Teng", title = "Electrical flows, {Laplacian} systems, and faster approximation of maximum flow in undirected graphs", crossref = "ACM:2011:SPA", pages = "273--282", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993674", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Friedmann:2011:SLB, author = "Oliver Friedmann and Thomas Dueholm Hansen and Uri Zwick", title = "Subexponential lower bounds for randomized pivoting rules for the simplex algorithm", crossref = "ACM:2011:SPA", pages = "283--292", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993675", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Haeupler:2011:ANC, author = "Bernhard Haeupler", title = "Analyzing network coding gossip made easy", crossref = "ACM:2011:SPA", pages = "293--302", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993676", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Chuzhoy:2011:AGC, author = "Julia Chuzhoy", title = "An algorithm for the graph crossing number problem", crossref = "ACM:2011:SPA", pages = "303--312", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993678", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Italiano:2011:IAM, author = "Giuseppe F. Italiano and Yahav Nussbaum and Piotr Sankowski and Christian Wulff-Nilsen", title = "Improved algorithms for min cut and max flow in undirected planar graphs", crossref = "ACM:2011:SPA", pages = "313--322", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993679", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Dinitz:2011:DSF, author = "Michael Dinitz and Robert Krauthgamer", title = "Directed spanners via flow-based linear programs", crossref = "ACM:2011:SPA", pages = "323--332", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993680", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Aaronson:2011:CCL, author = "Scott Aaronson and Alex Arkhipov", title = "The computational complexity of linear optics", crossref = "ACM:2011:SPA", pages = "333--342", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993682", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Brandao:2011:QTA, author = "Fernando G. S. L. Brand{\~a}o and Matthias Christandl and Jon Yard", title = "A quasipolynomial-time algorithm for the quantum separability problem", crossref = "ACM:2011:SPA", pages = "343--352", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993683", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Kempe:2011:PRE, author = "Julia Kempe and Thomas Vidick", title = "Parallel repetition of entangled games", crossref = "ACM:2011:SPA", pages = "353--362", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993684", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Sarma:2011:DVH, author = "Atish Das Sarma and Stephan Holzer and Liah Kor and Amos Korman and Danupon Nanongkai and Gopal Pandurangan and David Peleg and Roger Wattenhofer", title = "Distributed verification and hardness of distributed approximation", crossref = "ACM:2011:SPA", pages = "363--372", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993686", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Golab:2011:LID, author = "Wojciech Golab and Lisa Higham and Philipp Woelfel", title = "Linearizable implementations do not suffice for randomized distributed computation", crossref = "ACM:2011:SPA", pages = "373--382", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993687", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Kantor:2011:TWC, author = "Erez Kantor and Zvi Lotker and Merav Parter and David Peleg", title = "The topology of wireless communication", crossref = "ACM:2011:SPA", pages = "383--392", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993688", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Giakkoupis:2011:OPS, author = "George Giakkoupis and Nicolas Schabanel", title = "Optimal path search in small worlds: dimension matters", crossref = "ACM:2011:SPA", pages = "393--402", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993689", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Novocin:2011:LRA, author = "Andrew Novocin and Damien Stehl{\'e} and Gilles Villard", title = "An {LLL}-reduction algorithm with quasi-linear time complexity: extended abstract", crossref = "ACM:2011:SPA", pages = "403--412", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993691", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Khot:2011:NHA, author = "Subhash Khot and Dana Moshkovitz", title = "{NP}-hardness of approximately solving linear equations over reals", crossref = "ACM:2011:SPA", pages = "413--420", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993692", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Saraf:2011:BBI, author = "Shubhangi Saraf and Ilya Volkovich", title = "Black-box identity testing of depth-4 multilinear circuits", crossref = "ACM:2011:SPA", pages = "421--430", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993693", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Saxena:2011:BIT, author = "Nitin Saxena and C. Seshadhri", title = "Blackbox identity testing for bounded top fanin depth-3 circuits: the field doesn't matter", crossref = "ACM:2011:SPA", pages = "431--440", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993694", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Demaine:2011:CDH, author = "Erik D. Demaine and MohammadTaghi Hajiaghayi and Ken-ichi Kawarabayashi", title = "Contraction decomposition in $h$-minor-free graphs and algorithmic applications", crossref = "ACM:2011:SPA", pages = "441--450", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993696", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Kawarabayashi:2011:SAS, author = "Ken-ichi Kawarabayashi and Paul Wollan", title = "A simpler algorithm and shorter proof for the graph minor decomposition", crossref = "ACM:2011:SPA", pages = "451--458", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993697", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Bousquet:2011:MF, author = "Nicolas Bousquet and Jean Daligault and St{\'e}phan Thomass{\'e}", title = "Multicut is {FPT}", crossref = "ACM:2011:SPA", pages = "459--468", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993698", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Marx:2011:FPT, author = "D{\'a}niel Marx and Igor Razgon", title = "Fixed-parameter tractability of multicut parameterized by the size of the cutset", crossref = "ACM:2011:SPA", pages = "469--478", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993699", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Grohe:2011:FTS, author = "Martin Grohe and Ken-ichi Kawarabayashi and D{\'a}niel Marx and Paul Wollan", title = "Finding topological subgraphs is fixed-parameter tractable", crossref = "ACM:2011:SPA", pages = "479--488", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993700", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Kopparty:2011:CPF, author = "Swastik Kopparty", title = "On the complexity of powering in finite fields", crossref = "ACM:2011:SPA", pages = "489--498", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993702", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Chien:2011:ASH, author = "Steve Chien and Prahladh Harsha and Alistair Sinclair and Srikanth Srinivasan", title = "Almost settling the hardness of noncommutative determinant", crossref = "ACM:2011:SPA", pages = "499--508", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993703", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Burgisser:2011:GCT, author = "Peter B{\"u}rgisser and Christian Ikenmeyer", title = "Geometric complexity theory and tensor rank", crossref = "ACM:2011:SPA", pages = "509--518", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993704", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Barak:2011:RBD, author = "Boaz Barak and Zeev Dvir and Amir Yehudayoff and Avi Wigderson", title = "Rank bounds for design matrices with applications to combinatorial geometry and locally correctable codes", crossref = "ACM:2011:SPA", pages = "519--528", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993705", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Kleinberg:2011:MMA, author = "Jon Kleinberg and Sigal Oren", title = "Mechanisms for (mis)allocating scientific credit", crossref = "ACM:2011:SPA", pages = "529--538", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993707", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Cole:2011:IPS, author = "Richard Cole and Jos{\'e} R. Correa and Vasilis Gkatzelis and Vahab Mirrokni and Neil Olver", title = "Inner product spaces for {MinSum} coordination mechanisms", crossref = "ACM:2011:SPA", pages = "539--548", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993708", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Feige:2011:MDU, author = "Uriel Feige and Moshe Tennenholtz", title = "Mechanism design with uncertain inputs: (to err is human, to forgive divine)", crossref = "ACM:2011:SPA", pages = "549--558", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993709", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Patrascu:2011:DRU, author = "Mihai P{\u{a}}tra{\c{s}}cu and Mikkel Thorup", title = "Don't rush into a union: take time to find your roots", crossref = "ACM:2011:SPA", pages = "559--568", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993711", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Feldman:2011:UFA, author = "Dan Feldman and Michael Langberg", title = "A unified framework for approximating and clustering data", crossref = "ACM:2011:SPA", pages = "569--578", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993712", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Arya:2011:APM, author = "Sunil Arya and Guilherme D. da Fonseca and David M. Mount", title = "Approximate polytope membership queries", crossref = "ACM:2011:SPA", pages = "579--586", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993713", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Karande:2011:OBM, author = "Chinmay Karande and Aranyak Mehta and Pushkar Tripathi", title = "Online bipartite matching with unknown distributions", crossref = "ACM:2011:SPA", pages = "587--596", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993715", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Mahdian:2011:OBM, author = "Mohammad Mahdian and Qiqi Yan", title = "Online bipartite matching with random arrivals: an approach based on strongly factor-revealing {LPs}", crossref = "ACM:2011:SPA", pages = "597--606", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993716", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Adamaszek:2011:ATB, author = "Anna Adamaszek and Artur Czumaj and Matthias Englert and Harald R{\"a}cke", title = "Almost tight bounds for reordering buffer management", crossref = "ACM:2011:SPA", pages = "607--616", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993717", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Svensson:2011:SCS, author = "Ola Svensson", title = "{Santa Claus} schedules jobs on unrelated machines", crossref = "ACM:2011:SPA", pages = "617--626", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993718", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Indyk:2011:KMC, author = "Piotr Indyk and Eric Price", title = "{$K$}-median clustering, model-based compressive sensing, and sparse recovery for earth mover distance", crossref = "ACM:2011:SPA", pages = "627--636", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993720", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Bourgain:2011:BBE, author = "Jean Bourgain and Stephen J. Dilworth and Kevin Ford and Sergei V. Konyagin and Denka Kutzarova", title = "Breaking the $k^2$ barrier for explicit {RIP} matrices", crossref = "ACM:2011:SPA", pages = "637--644", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993721", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Karnin:2011:DCH, author = "Zohar S. Karnin", title = "Deterministic construction of a high dimensional $l_p$ section in $l_1^n$ for any $p < 2$", crossref = "ACM:2011:SPA", pages = "645--654", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993722", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Bodirsky:2011:STG, author = "Manuel Bodirsky and Michael Pinsker", title = "{Schaefer}'s theorem for graphs", crossref = "ACM:2011:SPA", pages = "655--664", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993724", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Yoshida:2011:OCT, author = "Yuichi Yoshida", title = "Optimal constant-time approximation algorithms and (unconditional) inapproximability results for every bounded-degree {CSP}", crossref = "ACM:2011:SPA", pages = "665--674", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993725", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Newman:2011:EPH, author = "Ilan Newman and Christian Sohler", title = "Every property of hyperfinite graphs is testable", crossref = "ACM:2011:SPA", pages = "675--684", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993726", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Valiant:2011:EUS, author = "Gregory Valiant and Paul Valiant", title = "Estimating the unseen: an $n / \log(n)$-sample estimator for entropy and support size, shown optimal via new {CLTs}", crossref = "ACM:2011:SPA", pages = "685--694", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993727", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Goyal:2011:CRN, author = "Vipul Goyal", title = "Constant round non-malleable protocols using one way functions", crossref = "ACM:2011:SPA", pages = "695--704", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993729", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Lin:2011:CRN, author = "Huijia Lin and Rafael Pass", title = "Constant-round non-malleable commitments from any one-way function", crossref = "ACM:2011:SPA", pages = "705--714", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993730", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Ajtai:2011:SCI, author = "Miklos Ajtai", title = "Secure computation with information leaking to an adversary", crossref = "ACM:2011:SPA", pages = "715--724", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993731", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Lewko:2011:HLK, author = "Allison Lewko and Mark Lewko and Brent Waters", title = "How to leak on key updates", crossref = "ACM:2011:SPA", pages = "725--734", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993732", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Woodruff:2011:NOP, author = "David P. Woodruff", title = "Near-optimal private approximation protocols via a black box transformation", crossref = "ACM:2011:SPA", pages = "735--744", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993733", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Kane:2011:FME, author = "Daniel M. Kane and Jelani Nelson and Ely Porat and David P. Woodruff", title = "Fast moment estimation in data streams in optimal space", crossref = "ACM:2011:SPA", pages = "745--754", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993735", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Sohler:2011:SEN, author = "Christian Sohler and David P. Woodruff", title = "Subspace embeddings for the {$L_1$}-norm with applications", crossref = "ACM:2011:SPA", pages = "755--764", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993736", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Lee:2011:NOD, author = "James R. Lee and Anastasios Sidiropoulos", title = "Near-optimal distortion bounds for embedding doubling spaces into {$L_1$}", crossref = "ACM:2011:SPA", pages = "765--772", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993737", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Fawzi:2011:LDN, author = "Omar Fawzi and Patrick Hayden and Pranab Sen", title = "From low-distortion norm embeddings to explicit uncertainty relations and efficient information locking", crossref = "ACM:2011:SPA", pages = "773--782", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993738", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Vondrak:2011:SFM, author = "Jan Vondr{\'a}k and Chandra Chekuri and Rico Zenklusen", title = "Submodular function maximization via the multilinear relaxation and contention resolution schemes", crossref = "ACM:2011:SPA", pages = "783--792", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993740", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Balcan:2011:LSF, author = "Maria-Florina Balcan and Nicholas J. A. Harvey", title = "Learning submodular functions", crossref = "ACM:2011:SPA", pages = "793--802", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993741", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Gupta:2011:PRC, author = "Anupam Gupta and Moritz Hardt and Aaron Roth and Jonathan Ullman", title = "Privately releasing conjunctions and the statistical query barrier", crossref = "ACM:2011:SPA", pages = "803--812", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993742", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Smith:2011:PPS, author = "Adam Smith", title = "Privacy-preserving statistical estimation with optimal convergence rates", crossref = "ACM:2011:SPA", pages = "813--822", year = "2011", DOI = "https://doi.org/10.1145/1993636.1993743", bibdate = "Tue Jun 7 18:53:27 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, } @InProceedings{Kelner:2012:FAM, author = "Jonathan A. Kelner and Gary L. Miller and Richard Peng", title = "Faster approximate multicommodity flow using quadratically coupled flows", crossref = "ACM:2012:SPA", pages = "1--18", year = "2012", DOI = "https://doi.org/10.1145/2213977.2213979", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "The maximum multicommodity flow problem is a natural generalization of the maximum flow problem to route multiple distinct flows. Obtaining a $1 - \epsilon$ approximation to the multicommodity flow problem on graphs is a well-studied problem. In this paper we present an adaptation of recent advances in single-commodity flow algorithms to this problem. As the underlying linear systems in the electrical problems of multicommodity flow problems are no longer Laplacians, our approach is tailored to generate specialized systems which can be preconditioned and solved efficiently using Laplacians. Given an undirected graph with $m$ edges and $k$ commodities, we give algorithms that find $1 - \epsilon$ approximate solutions to the maximum concurrent flow problem and maximum weighted multicommodity flow problem in time $O(m^{4/3} \poly(k, \epsilon^{-1}))$.", acknowledgement = ack-nhfb, } @InProceedings{Chakrabarti:2012:WCC, author = "Amit Chakrabarti and Lisa Fleischer and Christophe Weibel", title = "When the cut condition is enough: a complete characterization for multiflow problems in series-parallel networks", crossref = "ACM:2012:SPA", pages = "19--26", year = "2012", DOI = "https://doi.org/10.1145/2213977.2213980", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Let $G = (V, E)$ be a supply graph and $H = (V,F)$ a demand graph defined on the same set of vertices. An assignment of capacities to the edges of $G$ and demands to the edges of $H$ is said to satisfy the cut condition if for any cut in the graph, the total demand crossing the cut is no more than the total capacity crossing it. The pair $(G, H)$ is called cut-sufficient if for any assignment of capacities and demands that satisfy the cut condition, there is a multiflow routing the demands defined on $H$ within the network with capacities defined on $G$. We prove a previous conjecture, which states that when the supply graph $G$ is series-parallel, the pair (G,H) is cut-sufficient if and only if $(G, H)$ does not contain an odd spindle as a minor; that is, if it is impossible to contract edges of $G$ and delete edges of $G$ and $H$ so that $G$ becomes the complete bipartite graph $K_{2,p}$, with $p \geq 3$ odd, and $H$ is composed of a cycle connecting the $p$ vertices of degree $2$, and an edge connecting the two vertices of degree $p$. We further prove that if the instance is Eulerian --- that is, the demands and capacities are integers and the total of demands and capacities incident to each vertex is even --- then the multiflow problem has an integral solution. We provide a polynomial-time algorithm to find an integral solution in this case. In order to prove these results, we formulate properties of tight cuts (cuts for which the cut condition inequality is tight) in cut-sufficient pairs. We believe these properties might be useful in extending our results to planar graphs.", acknowledgement = ack-nhfb, } @InProceedings{Vegh:2012:SPA, author = "L{\'a}szl{\'o} A. V{\'e}gh", title = "Strongly polynomial algorithm for a class of minimum-cost flow problems with separable convex objectives", crossref = "ACM:2012:SPA", pages = "27--40", year = "2012", DOI = "https://doi.org/10.1145/2213977.2213981", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "A well-studied nonlinear extension of the minimum-cost flow problem is to minimize the objective $\Sigma_{i j \in E} C_{ij} (f_{ij})$ over feasible flows $f$, where on every arc $ij$ of the network, $C_{ij}$ is a convex function. We give a strongly polynomial algorithm for finding an exact optimal solution for a broad class of such problems. The key characteristic of this class is that an optimal solution can be computed exactly provided its support. This includes separable convex quadratic objectives and also certain market equilibria problems: Fisher's market with linear and with spending constraint utilities. We thereby give the first strongly polynomial algorithms for separable quadratic minimum-cost flows and for Fisher's market with spending constraint utilities, settling open questions posed e.g. in [15] and in [35], respectively. The running time is $O(m^4 \log m)$ for quadratic costs, $O(n^4 + n^2 (m + n \log n) \log n)$ for Fisher's markets with linear utilities and $O(m n^3 + m^2 (m + n \log n) \log m)$ for spending constraint utilities.", acknowledgement = ack-nhfb, } @InProceedings{Aaronson:2012:QMH, author = "Scott Aaronson and Paul Christiano", title = "Quantum money from hidden subspaces", crossref = "ACM:2012:SPA", pages = "41--60", year = "2012", DOI = "https://doi.org/10.1145/2213977.2213983", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Forty years ago, Wiesner pointed out that quantum mechanics raises the striking possibility of money that cannot be counterfeited according to the laws of physics. We propose the first quantum money scheme that is (1) public-key --- meaning that anyone can verify a banknote as genuine, not only the bank that printed it, and (2) cryptographically secure, under a ``classical'' hardness assumption that has nothing to do with quantum money. Our scheme is based on hidden subspaces, encoded as the zero-sets of random multivariate polynomials. A main technical advance is to show that the ``black-box'' version of our scheme, where the polynomials are replaced by classical oracles, is unconditionally secure. Previously, such a result had only been known relative to a quantum oracle (and even there, the proof was never published). Even in Wiesner's original setting --- quantum money that can only be verified by the bank --- we are able to use our techniques to patch a major security hole in Wiesner's scheme. We give the first private-key quantum money scheme that allows unlimited verifications and that remains unconditionally secure, even if the counterfeiter can interact adaptively with the bank. Our money scheme is simpler than previous public-key quantum money schemes, including a knot-based scheme of Farhi et al. The verifier needs to perform only two tests, one in the standard basis and one in the Hadamard basis --- matching the original intuition for quantum money, based on the existence of complementary observables. Our security proofs use a new variant of Ambainis's quantum adversary method, and several other tools that might be of independent interest.", acknowledgement = ack-nhfb, } @InProceedings{Vazirani:2012:CQD, author = "Umesh Vazirani and Thomas Vidick", title = "Certifiable quantum dice: or, true random number generation secure against quantum adversaries", crossref = "ACM:2012:SPA", pages = "61--76", year = "2012", DOI = "https://doi.org/10.1145/2213977.2213984", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We introduce a protocol through which a pair of quantum mechanical devices may be used to generate $n$ bits that are $\epsilon$-close in statistical distance from $n$ uniformly distributed bits, starting from a seed of $O(\log n \log 1 / \epsilon)$ uniform bits. The bits generated are certifiably random based only on a simple statistical test that can be performed by the user, and on the assumption that the devices do not communicate in the middle of each phase of the protocol. No other assumptions are placed on the devices' inner workings. A modified protocol uses a seed of $O(\log^3 n)$ uniformly random bits to generate $n$ bits that are $\poly^{-1}(n)$-indistinguishable from uniform even from the point of view of a quantum adversary who may have had prior access to the devices, and may be entangled with them.", acknowledgement = ack-nhfb, } @InProceedings{Belovs:2012:SPF, author = "Aleksandrs Belovs", title = "Span programs for functions with constant-sized $1$-certificates: extended abstract", crossref = "ACM:2012:SPA", pages = "77--84", year = "2012", DOI = "https://doi.org/10.1145/2213977.2213985", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Besides the Hidden Subgroup Problem, the second large class of quantum speed-ups is for functions with constant-sized 1-certificates. This includes the OR function, solvable by the Grover algorithm, the element distinctness, the triangle and other problems. The usual way to solve them is by quantum walk on the Johnson graph. We propose a solution for the same problems using span programs. The span program is a computational model equivalent to the quantum query algorithm in its strength, and yet very different in its outfit. We prove the power of our approach by designing a quantum algorithm for the triangle problem with query complexity $O(n^{35/27})$ that is better than $O(n^{13/10})$ of the best previously known algorithm by Magniez et al.", acknowledgement = ack-nhfb, } @InProceedings{Larsen:2012:CPC, author = "Kasper Green Larsen", title = "The cell probe complexity of dynamic range counting", crossref = "ACM:2012:SPA", pages = "85--94", year = "2012", DOI = "https://doi.org/10.1145/2213977.2213987", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "In this paper we develop a new technique for proving lower bounds on the update time and query time of dynamic data structures in the cell probe model. With this technique, we prove the highest lower bound to date for any explicit problem, namely a lower bound of $t_q = \Omega((\lg n / \lg (wt_u))^2)$. Here $n$ is the number of update operations, $w$ the cell size, $t_q$ the query time and t$_u$ the update time. In the most natural setting of cell size $w = \Theta(\lg n)$, this gives a lower bound of $t_q = \Omega((\lg n / \lg \lg n)^2)$ for any polylogarithmic update time. This bound is almost a quadratic improvement over the highest previous lower bound of $\Omega(\lg n)$, due to Patrascu and Demaine [SICOMP'06]. We prove our lower bound for the fundamental problem of weighted orthogonal range counting. In this problem, we are to support insertions of two-dimensional points, each assigned a $\Theta(\lg n)$-bit integer weight. A query to this problem is specified by a point $q = (x, y)$, and the goal is to report the sum of the weights assigned to the points dominated by $q$, where a point $(x',y')$ is dominated by $q$ if $x' \leq x$ and $y' \leq y$. In addition to being the highest cell probe lower bound to date, our lower bound is also tight for data structures with update time $t_u = \Omega(\lg^{2 + \epsilon} n)$, where $\epsilon > 0$ is an arbitrarily small constant.", acknowledgement = ack-nhfb, } @InProceedings{Fiorini:2012:LVS, author = "Samuel Fiorini and Serge Massar and Sebastian Pokutta and Hans Raj Tiwary and Ronald de Wolf", title = "Linear vs. semidefinite extended formulations: exponential separation and strong lower bounds", crossref = "ACM:2012:SPA", pages = "95--106", year = "2012", DOI = "https://doi.org/10.1145/2213977.2213988", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We solve a 20-year old problem posed by Yannakakis and prove that there exists no polynomial-size linear program (LP) whose associated polytope projects to the traveling salesman polytope, even if the LP is not required to be symmetric. Moreover, we prove that this holds also for the cut polytope and the stable set polytope. These results were discovered through a new connection that we make between one-way quantum communication protocols and semidefinite programming reformulations of LPs.", acknowledgement = ack-nhfb, } @InProceedings{Goel:2012:PCA, author = "Gagan Goel and Vahab Mirrokni and Renato Paes Leme", title = "Polyhedral clinching auctions and the {AdWords} polytope", crossref = "ACM:2012:SPA", pages = "107--122", year = "2012", DOI = "https://doi.org/10.1145/2213977.2213990", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "A central issue in applying auction theory in practice is the problem of dealing with budget-constrained agents. A desirable goal in practice is to design incentive compatible, individually rational, and Pareto optimal auctions while respecting the budget constraints. Achieving this goal is particularly challenging in the presence of nontrivial combinatorial constraints over the set of feasible allocations. Toward this goal and motivated by AdWords auctions, we present an auction for polymatroidal environments satisfying the above properties. Our auction employs a novel clinching technique with a clean geometric description and only needs an oracle access to the submodular function defining the polymatroid. As a result, this auction not only simplifies and generalizes all previous results, it applies to several new applications including AdWords Auctions, bandwidth markets, and video on demand. In particular, our characterization of the AdWords auction as polymatroidal constraints might be of independent interest. This allows us to design the first mechanism for Ad Auctions taking into account simultaneously budgets, multiple keywords and multiple slots. We show that it is impossible to extend this result to generic polyhedral constraints. This also implies an impossibility result for multi-unit auctions with decreasing marginal utilities in the presence of budget constraints.", acknowledgement = ack-nhfb, } @InProceedings{Kleinberg:2012:MPI, author = "Robert Kleinberg and Seth Matthew Weinberg", title = "Matroid prophet inequalities", crossref = "ACM:2012:SPA", pages = "123--136", year = "2012", DOI = "https://doi.org/10.1145/2213977.2213991", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Consider a gambler who observes a sequence of independent, non-negative random numbers and is allowed to stop the sequence at any time, claiming a reward equal to the most recent observation. The famous prophet inequality of Krengel, Sucheston, and Garling asserts that a gambler who knows the distribution of each random variable can achieve at least half as much reward, in expectation, as a ``prophet'' who knows the sampled values of each random variable and can choose the largest one. We generalize this result to the setting in which the gambler and the prophet are allowed to make more than one selection, subject to a matroid constraint. We show that the gambler can still achieve at least half as much reward as the prophet; this result is the best possible, since it is known that the ratio cannot be improved even in the original prophet inequality, which corresponds to the special case of rank-one matroids. Generalizing the result still further, we show that under an intersection of $p$ matroid constraints, the prophet's reward exceeds the gambler's by a factor of at most $O(p)$, and this factor is also tight. Beyond their interest as theorems about pure online algorithms or optimal stopping rules, these results also have applications to mechanism design. Our results imply improved bounds on the ability of sequential posted-price mechanisms to approximate optimal mechanisms in both single-parameter and multi-parameter Bayesian settings. In particular, our results imply the first efficiently computable constant-factor approximations to the Bayesian optimal revenue in certain multi-parameter settings.", acknowledgement = ack-nhfb, } @InProceedings{Devanur:2012:OMC, author = "Nikhil R. Devanur and Kamal Jain", title = "Online matching with concave returns", crossref = "ACM:2012:SPA", pages = "137--144", year = "2012", DOI = "https://doi.org/10.1145/2213977.2213992", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We consider a significant generalization of the AdWords problem by allowing arbitrary concave returns, and we characterize the optimal competitive ratio achievable. The problem considers a sequence of items arriving online that have to be allocated to agents, with different agents bidding different amounts. The objective function is the sum, over each agent i, of a monotonically non-decreasing concave function $M_i: R_? + \to R_+$ of the total amount allocated to $i$. All variants of online matching problems (including the AdWords problem) studied in the literature consider the special case of budgeted linear functions, that is, functions of the form $M_i(u_i) = \min\{u_i, B_i\}$ for some constant $B_i$. The distinguishing feature of this paper is in allowing arbitrary concave returns. The main result of this paper is that for each concave function $M$, there exists a constant $F(M) \leq 1$ such that: there exists an algorithm with competitive ratio of $\min_i F(M_i)$, independent of the sequence of items. No algorithm has a competitive ratio larger than $F(M)$ over all instances with $M_i = M$ for all $i$. Our algorithm is based on the primal-dual paradigm and makes use of convex programming duality. The upper bounds are obtained by formulating the task of finding the right counterexample as an optimization problem. This path takes us through the calculus of variations which deals with optimizing over continuous functions. The algorithm and the upper bound are related to each other via a set of differential equations, which points to a certain kind of duality between them.", acknowledgement = ack-nhfb, } @InProceedings{Arora:2012:CNM, author = "Sanjeev Arora and Rong Ge and Ravindran Kannan and Ankur Moitra", title = "Computing a nonnegative matrix factorization --- provably", crossref = "ACM:2012:SPA", pages = "145--162", year = "2012", DOI = "https://doi.org/10.1145/2213977.2213994", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "The Nonnegative Matrix Factorization (NMF) problem has a rich history spanning quantum mechanics, probability theory, data analysis, polyhedral combinatorics, communication complexity, demography, chemometrics, etc. In the past decade NMF has become enormously popular in machine learning, where the factorization is computed using a variety of local search heuristics. Vavasis recently proved that this problem is NP-complete. We initiate a study of when this problem is solvable in polynomial time. Consider a nonnegative $m \times n$ matrix $M$ and a target inner-dimension $r$. Our results are the following: --- We give a polynomial-time algorithm for exact and approximate NMF for every constant $r$. Indeed NMF is most interesting in applications precisely when $r$ is small. We complement this with a hardness result, that if exact NMF can be solved in time $(n m)^{o(r)}$, 3-SAT has a sub-exponential time algorithm. Hence, substantial improvements to the above algorithm are unlikely. --- We give an algorithm that runs in time polynomial in n, $m$ and $r$ under the separability condition identified by Donoho and Stodden in 2003. The algorithm may be practical since it is simple and noise tolerant (under benign assumptions). Separability is believed to hold in many practical settings. To the best of our knowledge, this last result is the first polynomial-time algorithm that provably works under a non-trivial condition on the input matrix and we believe that this will be an interesting and important direction for future work.", acknowledgement = ack-nhfb, } @InProceedings{Forbes:2012:ITT, author = "Michael A. Forbes and Amir Shpilka", title = "On identity testing of tensors, low-rank recovery and compressed sensing", crossref = "ACM:2012:SPA", pages = "163--172", year = "2012", DOI = "https://doi.org/10.1145/2213977.2213995", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We study the problem of obtaining efficient, deterministic, {\em black-box polynomial identity testing algorithms\/} for depth-$3$ set-multilinear circuits (over arbitrary fields). This class of circuits has an efficient, deterministic, white-box polynomial identity testing algorithm (due to Raz and Shpilka [36]), but has no known such black-box algorithm. We recast this problem as a question of finding a low-dimensional subspace $H$, spanned by rank $1$ tensors, such that any non-zero tensor in the dual space $\ker(H)$ has high rank. We obtain explicit constructions of essentially optimal-size hitting sets for tensors of degree $2$ (matrices), and obtain the first quasi-polynomial sized hitting sets for arbitrary tensors.\par We also show connections to the task of performing low-rank recovery of matrices, which is studied in the field of compressed sensing. Low-rank recovery asks (say, over $R$) to recover a matrix $M$ from few measurements, under the promise that $M$ is rank $\leq r$. In this work, we restrict our attention to recovering matrices that are exactly rank $\leq r$ using deterministic, non-adaptive, linear measurements, that are free from noise. Over $R$, we provide a set (of size $4 n r$) of such measurements, from which $M$ can be recovered in $O(r n^2 + r^3 n)$ field operations, and the number of measurements is essentially optimal. Further, the measurements can be taken to be all rank-$1$ matrices, or all sparse matrices. To the best of our knowledge no explicit constructions with those properties were known prior to this work.\par We also give a more formal connection between low-rank recovery and the task of {\em sparse (vector) recovery\/}: any sparse-recovery algorithm that exactly recovers vectors of length $n$ and sparsity $2 r$, using $m$ non-adaptive measurements, yields a low-rank recovery scheme for exactly recovering $n \times n$ matrices of rank $\leq r$, making $2 n m$ non-adaptive measurements. Furthermore, if the sparse-recovery algorithm runs in time $\tau$, then the low-rank recovery algorithm runs in time $O(r n^2 + n \tau)$. We obtain this reduction using linear-algebraic techniques, and not using convex optimization, which is more commonly seen in compressed sensing algorithms.\par Finally, we also make a connection to {\em rank-metric codes}, as studied in coding theory. These are codes with codewords consisting of matrices (or tensors) where the distance of matrices $M$ and $N$ is rank $(M - N)$, as opposed to the usual Hamming metric. We obtain essentially optimal-rate codes over matrices, and provide an efficient decoding algorithm. We obtain codes over tensors as well, with poorer rate, but still with efficient decoding.", acknowledgement = ack-nhfb, } @InProceedings{Grohe:2012:STI, author = "Martin Grohe and D{\'a}niel Marx", title = "Structure theorem and isomorphism test for graphs with excluded topological subgraphs", crossref = "ACM:2012:SPA", pages = "173--192", year = "2012", DOI = "https://doi.org/10.1145/2213977.2213996", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We generalize the structure theorem of Robertson and Seymour for graphs excluding a fixed graph $H$ as a minor to graphs excluding $H$ as a topological subgraph. We prove that for a fixed H, every graph excluding $H$ as a topological subgraph has a tree decomposition where each part is either ``almost embeddable'' to a fixed surface or has bounded degree with the exception of a bounded number of vertices. Furthermore, such a decomposition is computable by an algorithm that is fixed-parameter tractable with parameter $|H|$. We present two algorithmic applications of our structure theorem. To illustrate the mechanics of a ``typical'' application of the structure theorem, we show that on graphs excluding $H$ as a topological subgraph, Partial Dominating Set (find $k$ vertices whose closed neighborhood has maximum size) can be solved in time $f(H,k) \cdot n^{O(1)}$ time. More significantly, we show that on graphs excluding $H$ as a topological subgraph, Graph Isomorphism can be solved in time $n^{f(H)}$. This result unifies and generalizes two previously known important polynomial-time solvable cases of Graph Isomorphism: bounded-degree graphs and H-minor free graphs. The proof of this result needs a generalization of our structure theorem to the context of invariant treelike decomposition.", acknowledgement = ack-nhfb, } @InProceedings{Hrubes:2012:SPD, author = "Pavel Hrubes and Iddo Tzameret", title = "Short proofs for the determinant identities", crossref = "ACM:2012:SPA", pages = "193--212", year = "2012", DOI = "https://doi.org/10.1145/2213977.2213998", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We study arithmetic proof systems $P_c(F)$ and $P_f(F)$ operating with arithmetic circuits and arithmetic formulas, respectively, that prove polynomial identities over a field $F$. We establish a series of structural theorems about these proof systems, the main one stating that $P_c(F)$ proofs can be balanced: if a polynomial identity of syntactic degree $d$ and depth $k$ has a $P_c(F)$ proof of size $s$, then it also has a $P_c(F)$ proof of size $\poly(s,d)$ and depth $O(k + \log^2 d + \log d \cdot \log s)$. As a corollary, we obtain a quasipolynomial simulation of $P_c(F)$ by $P_f(F)$, for identities of a polynomial syntactic degree.\par Using these results we obtain the following: consider the identities:\par $$\det(X Y) = \det(X) \cdot \det(Y) \quad {\rm and} \quad \det(Z) = z_{11} \cdots z_{nn},$$\par where $X$, $Y$ and $Z$ are $n \times n$ square matrices and $Z$ is a triangular matrix with $z_{11}, \ldots{}, z_{nn}$ on the diagonal (and $\det$ is the determinant polynomial). Then we can construct a polynomial-size arithmetic circuit $\det$ such that the above identities have $P_c(F)$ proofs of polynomial-size and $O(\log^2 n)$ depth. Moreover, there exists an arithmetic formula det of size $n^{O(\log n)}$ such that the above identities have $P_f(F)$ proofs of size $n^{O(\log n)}$.\par This yields a solution to a basic open problem in propositional proof complexity, namely, whether there are polynomial-size NC$^2$-Frege proofs for the determinant identities and the hard matrix identities, as considered, e.g. in Soltys and Cook (2004) (cf., Beame and Pitassi (1998)). We show that matrix identities like $A B = I \to B A = I$ (for matrices over the two element field) as well as basic properties of the determinant have polynomial-size NC$^2$-Frege proofs, and quasipolynomial-size Frege proofs.", acknowledgement = ack-nhfb, } @InProceedings{Beame:2012:TST, author = "Paul Beame and Christopher Beck and Russell Impagliazzo", title = "Time-space tradeoffs in resolution: superpolynomial lower bounds for superlinear space", crossref = "ACM:2012:SPA", pages = "213--232", year = "2012", DOI = "https://doi.org/10.1145/2213977.2213999", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We give the first time-space tradeoff lower bounds for Resolution proofs that apply to superlinear space. In particular, we show that there are formulas of size $N$ that have Resolution refutations of space and size each roughly $N^{\log 2 N}$ (and like all formulas have Resolution refutations of space $N$) for which any Resolution refutation using space $S$ and length $T$ requires $T \geq (N^{0.58 \log 2 N} /S)^{\Omega(\log \log N/\log \log \log N)}$. By downward translation, a similar tradeoff applies to all smaller space bounds. We also show somewhat stronger time-space tradeoff lower bounds for Regular Resolution, which are also the first to apply to superlinear space. Namely, for any space bound $S$ at most $2^{o(N^{1/4})}$ there are formulas of size $N$, having clauses of width $4$, that have Regular Resolution proofs of space $S$ and slightly larger size $T = O(NS)$, but for which any Regular Resolution proof of space $S^{1 - \epsilon}$ requires length $T^{\Omega(\log \log N / \log \log \log N)}$.", acknowledgement = ack-nhfb, } @InProceedings{Huynh:2012:VSP, author = "Trinh Huynh and Jakob Nordstrom", title = "On the virtue of succinct proofs: amplifying communication complexity hardness to time-space trade-offs in proof complexity", crossref = "ACM:2012:SPA", pages = "233--248", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214000", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "An active line of research in proof complexity over the last decade has been the study of proof space and trade-offs between size and space. Such questions were originally motivated by practical SAT solving, but have also led to the development of new theoretical concepts in proof complexity of intrinsic interest and to results establishing nontrivial relations between space and other proof complexity measures. By now, the resolution proof system is fairly well understood in this regard, as witnessed by a sequence of papers leading up to [Ben-Sasson and Nordstrom 2008, 2011] and [Beame, Beck, and Impagliazzo 2012]. However, for other relevant proof systems in the context of SAT solving, such as polynomial calculus (PC) and cutting planes (CP), very little has been known. Inspired by [BN08, BN11], we consider CNF encodings of so-called pebble games played on graphs and the approach of making such pebbling formulas harder by simple syntactic modifications. We use this paradigm of hardness amplification to make progress on the relatively longstanding open question of proving time-space trade-offs for PC and CP. Namely, we exhibit a family of modified pebbling formulas $\{F_n\}$ such that: --- The formulas $F_n$ have size $O(n)$ and width $O(1)$. --- They have proofs in length $O(n)$ in resolution, which generalize to both PC and CP. --- Any refutation in CP or PCR (a generalization of PC) in length $L$ and space $s$ must satisfy $s \log L > \approx \sqrt [4]{n}$. A crucial technical ingredient in these results is a new two-player communication complexity lower bound for composed search problems in terms of block sensitivity, a contribution that we believe to be of independent interest.", acknowledgement = ack-nhfb, } @InProceedings{Ajtai:2012:DVN, author = "Mikl{\'o}s Ajtai", title = "Determinism versus nondeterminism with arithmetic tests and computation: extended abstract", crossref = "ACM:2012:SPA", pages = "249--268", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214001", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "For each natural number $d$ we consider a finite structure $M_d$ whose universe is the set of all $0, 1$-sequence of length $n = 2^d$, each representing a natural number in the set $\{0, 1, \ldots{}, 2^n - 1\}$ in binary form. The operations included in the structure are the four constants $0$, $1$, $2^n - 1$, $n$, multiplication and addition modulo $2^n$, the unary function $\min\{2^x, 2^n - 1\}$, the binary functions $\lfloor x / y \rfloor$ (with $\lfloor x / 0 \rfloor = 0$), $\max(x, y)$, $\min(x, y)$, and the boolean vector operations $\wedge$, $\vee$, [??not??] defined on $0, 1$ sequences of length $n$ by performing the operations on all components simultaneously. These are essentially the arithmetic operations that can be performed on a RAM, with wordlength $n$, by a single instruction. We show that there exists a term (that is, an algebraic expression) $F(x,y)$ built up from the mentioned operations, with the only free variables $x$, $y$, such that for all terms $G(y)$, which is also built up from the mentioned operations, the following holds. For infinitely many positive integers $d$, there exists an $a \in M_d$ such that the following two statements are not equivalent: (i) $M_d \models \exists x, F(x,a)$, (ii) $M_d \models G(a) = 0$. In other words, the question whether an existential statement, depending on the parameter $a \in M_d$ is true or not, cannot be decided by evaluating an algebraic expression at $a$.\par Another way of formulating the theorem, in a slightly stronger form, is, that over the structures $M_d$, quantifier elimination is not possible in the following sense. Let $\cal M$ be a first-order language with equality, containing function symbols for all of the mentioned arithmetic operations. Then there exists an existential first-order formula $\phi(y)$ of $\cal M$, containing a single existential quantifier and the only free variable $y$, such that for each propositional formula $P(y)$ of $\cal M$, we have that for infinitely many positive integers $d$, $\phi(y)$ and $P(y)$ are not equivalent on $M_d$, that is, $M_d \models {\em [not]} \forall y$, $\phi(y) \leftrightarrow P(y)$.\par We also show that the theorem, in both forms, remains true if the binary operation $\min\{x^y, 2^n - 1\}$ is added to the structure $M_d$. A general theorem is proved as well, which describes sufficient conditions for a set of operations on a sequence of structures $K_d$, $d = 1, 2, \ldots{}$ which guarantees that the analogues of the mentioned theorems holds for the structures $K_d$ too.", acknowledgement = ack-nhfb, } @InProceedings{Heilman:2012:SPC, author = "Steven Heilman and Aukosh Jagannath and Assaf Naor", title = "Solution of the propeller conjecture in {$\mathbb{R}^3$}", crossref = "ACM:2012:SPA", pages = "269--276", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214003", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "It is shown that every measurable partition $\{A_1, \ldots{}, A_k\}$ of $\mathbb{R}^3$ satisfies:\par $$\sum_{i = 1}^k || \int_{A i} x e^{-1/2||x||^2_2} \, dx||_2^2 \leq 9 \pi ^2$$.\par Let $\{P_1, P_2, P_3\}$ be the partition of $\mathbb{R}^2$ into $120^\circ$ sectors centered at the origin. The bound (1) is sharp, with equality holding if $A_i = P_i \times \mathbb{R}$ for $i \in \{1, 2, 3\}$ and $A_i = \emptyset$ for $i \in \{4, \ldots{}, k\}$. This settles positively the 3-dimensional Propeller Conjecture of Khot and Naor (FOCS 2008). The proof of (1) reduces the problem to a finite set of numerical inequalities which are then verified with full rigor in a computer-assisted fashion. The main consequence (and motivation) of (1) is complexity-theoretic: the Unique Games hardness threshold of the Kernel Clustering problem with $4 \times 4$ centered and spherical hypothesis matrix equals $2 \pi /3$.", acknowledgement = ack-nhfb, } @InProceedings{Khot:2012:LHC, author = "Subhash A. Khot and Preyas Popat and Nisheeth K. Vishnoi", title = "$2^{\log^{1 - \epsilon} n}$ hardness for the closest vector problem with preprocessing", crossref = "ACM:2012:SPA", pages = "277--288", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214004", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We prove that for an arbitrarily small constant $\epsilon > 0$, assuming NP $\not\subseteq$ DTIME $(2^{\log^{O(1 / \epsilon) n}})$, the preprocessing versions of the closest vector problem and the nearest codeword problem are hard to approximate within a factor better than $2^{\log^{1 - \epsilon} n}$. This improves upon the previous hardness factor of $(\log n)^\delta$ for some $\delta > 0$ due to [AKKV05].", acknowledgement = ack-nhfb, } @InProceedings{ODonnell:2012:NPN, author = "Ryan O'Donnell and John Wright", title = "A new point of {NP}-hardness for unique games", crossref = "ACM:2012:SPA", pages = "289--306", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214005", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We show that distinguishing $1/2$-satisfiable Unique-Games instances from $(3/8 + \epsilon)$-satisfiable instances is NP-hard (for all $\epsilon > 0$). A consequence is that we match or improve the best known $c$ vs. $s$ NP-hardness result for Unique-Games for all values of $c$ (except for $c$ very close to $0$). For these $c$, ours is the first hardness result showing that it helps to take the alphabet size larger than $2$. Our NP-hardness reductions are quasilinear-size and thus show nearly full exponential time is required, assuming the ETH.", acknowledgement = ack-nhfb, } @InProceedings{Barak:2012:HSS, author = "Boaz Barak and Fernando G. S. L. Brandao and Aram W. Harrow and Jonathan Kelner and David Steurer and Yuan Zhou", title = "Hypercontractivity, sum-of-squares proofs, and their applications", crossref = "ACM:2012:SPA", pages = "307--326", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214006", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We study the computational complexity of approximating the $2$-to-$q$ norm of linear operators (defined as $||A||_{2 \to q} = \max_{v \neq 0} ||A v||_q / ||v||_2$) for $q > 2$, as well as connections between this question and issues arising in quantum information theory and the study of Khot's Unique Games Conjecture (UGC). We show the following: For any constant even integer $q \geq 4$, a graph $G$ is a small-set expander if and only if the projector into the span of the top eigenvectors of $G$'s adjacency matrix has bounded $2 \to q$ norm. As a corollary, a good approximation to the $2 \to q$ norm will refute the Small-Set Expansion Conjecture --- a close variant of the UGC. We also show that such a good approximation can be obtained in $\exp(n^{2 / q})$ time, thus obtaining a different proof of the known subexponential algorithm for Small-Set-Expansion. Constant rounds of the ``Sum of Squares'' semidefinite programming hierarchy certify an upper bound on the $2 \to 4$ norm of the projector to low degree polynomials over the Boolean cube, as well certify the unsatisfiability of the ``noisy cube'' and ``short code'' based instances of Unique-Games considered by prior works. This improves on the previous upper bound of $\exp(\log^{O(1)} n)$ rounds (for the ``short code''), as well as separates the ``Sum of Squares'' / ``Lasserre'' hierarchy from weaker hierarchies that were known to require $\omega(1)$ rounds. We show reductions between computing the $2 \to 4$ norm and computing the injective tensor norm of a tensor, a problem with connections to quantum information theory. Three corollaries are: (i) the $2 \to 4$ norm is NP-hard to approximate to precision inverse-polynomial in the dimension, (ii) the $2 \to 4$ norm does not have a good approximation (in the sense above) unless 3-SAT can be solved in time $\exp(\sqrt n \poly \log (n))$, and (iii) known algorithms for the quantum separability problem imply a non-trivial additive approximation for the $2 \to 4$ norm.", acknowledgement = ack-nhfb, } @InProceedings{Efremenko:2012:IRL, author = "Klim Efremenko", title = "From irreducible representations to locally decodable codes", crossref = "ACM:2012:SPA", pages = "327--338", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214008", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "A $q$-query Locally Decodable Code (LDC) is an error-correcting code that allows to read any particular symbol of the message by reading only $q$ symbols of the codeword even if the codeword is adversary corrupted. In this paper we present a new approach for the construction of LDCs. We show that if there exists an irreducible representation $(\rho, V)$ of $G$ and $q$ elements $g_1$, $g_2$, \ldots{}, $g_q$ in $G$ such that there exists a linear combination of matrices $\rho(g_i)$ that is of rank one, then we can construct a $q$-query Locally Decodable Code $C: V \to F^G$. We show the potential of this approach by constructing constant query LDCs of sub-exponential length matching the best known constructions.", acknowledgement = ack-nhfb, } @InProceedings{Guruswami:2012:FCF, author = "Venkatesan Guruswami and Chaoping Xing", title = "Folded codes from function field towers and improved optimal rate list decoding", crossref = "ACM:2012:SPA", pages = "339--350", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214009", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We give a new construction of algebraic codes which are efficiently list decodable from a fraction $1 - R - \epsilon$ of adversarial errors where $R$ is the rate of the code, for any desired positive constant $\epsilon$. The worst-case list size output by the algorithm is $O(1 / \epsilon)$, matching the existential bound for random codes up to constant factors. Further, the alphabet size of the codes is a constant depending only on $\epsilon$ --- it can be made $\exp(\tilde{O}(1 / \epsilon^2))$ which is not much worse than the non-constructive $\exp(1 / \epsilon)$ bound of random codes. The code construction is Monte Carlo and has the claimed list decoding property with high probability. Once the code is (efficiently) sampled, the encoding/decoding algorithms are deterministic with a running time $O_{\epsilon} (N^c)$ for an absolute constant $c$, where $N$ is the code's block length. Our construction is based on a careful combination of a linear-algebraic approach to list decoding folded codes from towers of function fields, with a special form of subspace-evasive sets. Instantiating this with the explicit ``asymptotically good'' Garcia--Stichtenoth (GS for short) tower of function fields yields the above parameters. To illustrate the method in a simpler setting, we also present a construction based on Hermitian function fields, which offers similar guarantees with a list-size and alphabet size polylogarithmic in the block length $N$. In comparison, algebraic codes achieving the optimal trade-off between list decodability and rate based on folded Reed--Solomon codes have a decoding complexity of $N^{\Omega(1 / \epsilon)}$, an alphabet size of $N^{\Omega(1 / \epsilon 2)}$, and a list size of $O(1 / \epsilon^2)$ (even after combination with subspace-evasive sets). Thus we get an improvement over the previous best bounds in all three aspects simultaneously, and are quite close to the existential random coding bounds. Along the way, we shed light on how to use automorphisms of certain function fields to enable list decoding of the folded version of the associated algebraic-geometric codes.", acknowledgement = ack-nhfb, } @InProceedings{Dvir:2012:SES, author = "Zeev Dvir and Shachar Lovett", title = "Subspace evasive sets", crossref = "ACM:2012:SPA", pages = "351--358", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214010", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We construct explicit subspace-evasive sets. These are subsets of $F^n$ of size $|F|^{(1- \epsilon)n}$ whose intersection with any $k$-dimensional subspace is bounded by a constant $c(k, \epsilon)$. This problem was raised by Guruswami (CCC 2011) as it leads to optimal rate list-decodable codes of constant list size. The main technical ingredient is the construction of $k$ low-degree polynomials whose common set of zeros has small intersection with any $k$-dimensional subspace.", acknowledgement = ack-nhfb, } @InProceedings{Kaufman:2012:ETR, author = "Tali Kaufman and Alexander Lubotzky", title = "Edge transitive {Ramanujan} graphs and symmetric {LDPC} good codes", crossref = "ACM:2012:SPA", pages = "359--366", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214011", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We present the first explicit construction of a binary symmetric code with constant rate and constant distance (i.e., good code). Moreover, the code is LDPC and its constraint space is generated by the orbit of one constant weight constraint under the group action. Our construction provides the first symmetric LDPC good codes. In particular, it solves the main open problem raised by Kaufman and Wigderson {8}.", acknowledgement = ack-nhfb, } @InProceedings{Makarychev:2012:AAS, author = "Konstantin Makarychev and Yury Makarychev and Aravindan Vijayaraghavan", title = "Approximation algorithms for semi-random partitioning problems", crossref = "ACM:2012:SPA", pages = "367--384", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214013", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "In this paper, we propose and study a new semi-random model for graph partitioning problems. We believe that it captures many properties of real-world instances. The model is more flexible than the semi-random model of Feige and Kilian and planted random model of Bui, Chaudhuri, Leighton and Sipser. We develop a general framework for solving semi-random instances and apply it to several problems of interest. We present constant factor bi-criteria approximation algorithms for semi-random instances of the Balanced Cut, Multicut, Min Uncut, Sparsest Cut and Small Set Expansion problems. We also show how to almost recover the optimal solution if the instance satisfies an additional expanding condition. Our algorithms work in a wider range of parameters than most algorithms for previously studied random and semi-random models. Additionally, we study a new planted algebraic expander model and develop constant factor bi-criteria approximation algorithms for graph partitioning problems in this model.", acknowledgement = ack-nhfb, } @InProceedings{Sharathkumar:2012:NLT, author = "R. Sharathkumar and Pankaj K. Agarwal", title = "A near-linear time $\epsilon$-approximation algorithm for geometric bipartite matching", crossref = "ACM:2012:SPA", pages = "385--394", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214014", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "For point sets $A, B \subset \mathbb{R}^d$, $|A| = |B| = n$, and for a parameter $\epsilon > 0$, we present an algorithm that computes, in $O(n \poly(\log n, 1 / \epsilon))$ time, an $\epsilon$-approximate perfect matching of $A$ and $B$ with high probability; the previously best known algorithm takes $\Omega(n^{3/2})$ time. We approximate the L$_p$-norm using a distance function, $d(\cdot,\cdot)$ based on a randomly shifted quad-tree. The algorithm iteratively generates an approximate minimum-cost augmenting path under $d(\cdot,\cdot)$ in time proportional to the length of the path. We show that the total length of the augmenting paths generated by the algorithm is $O((n / \epsilon)\log n)$, implying that the running time of our algorithm is $O(n \poly(\log n, 1 / \epsilon))$.", acknowledgement = ack-nhfb, } @InProceedings{Abraham:2012:UPD, author = "Ittai Abraham and Ofer Neiman", title = "Using petal-decompositions to build a low stretch spanning tree", crossref = "ACM:2012:SPA", pages = "395--406", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214015", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We prove that any graph $G = (V, E)$ with $n$ points and $m$ edges has a spanning tree $T$ such that $\sum_{(u,v) \in E(G)} d_T(u,v) = O(m \log n \log \log n)$. Moreover such a tree can be found in time $O(m \log n \log \log n)$. Our result is obtained using a new petal-decomposition approach which guarantees that the radius of each cluster in the tree is at most $4$ times the radius of the induced subgraph of the cluster in the original graph.", acknowledgement = ack-nhfb, } @InProceedings{Brunsch:2012:ISA, author = "Tobias Brunsch and Heiko R{\"o}glin", title = "Improved smoothed analysis of multiobjective optimization", crossref = "ACM:2012:SPA", pages = "407--426", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214016", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We present several new results about smoothed analysis of multiobjective optimization problems. Motivated by the discrepancy between worst-case analysis and practical experience, this line of research has gained a lot of attention in the last decade. We consider problems in which $d$ linear and one arbitrary objective function are to be optimized over a set $S \subseteq \{0, 1\}^n$ of feasible solutions. We improve the previously best known bound for the smoothed number of Pareto-optimal solutions to $O(n^{2d} \phi^d)$, where $\phi$ denotes the perturbation parameter. Additionally, we show that for any constant $c$ the $c$-th moment of the smoothed number of Pareto-optimal solutions is bounded by $O((n^{2d} \phi^d)^c)$. This improves the previously best known bounds significantly. Furthermore, we address the criticism that the perturbations in smoothed analysis destroy the zero-structure of problems by showing that the smoothed number of Pareto-optimal solutions remains polynomially bounded even for zero-preserving perturbations. This broadens the class of problems captured by smoothed analysis and it has consequences for non-linear objective functions. One corollary of our result is that the smoothed number of Pareto-optimal solutions is polynomially bounded for polynomial objective functions.", acknowledgement = ack-nhfb, } @InProceedings{Leonardi:2012:PFA, author = "Stefano Leonardi and Tim Roughgarden", title = "Prior-free auctions with ordered bidders", crossref = "ACM:2012:SPA", pages = "427--434", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214018", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Prior-free auctions are robust auctions that assume no distribution over bidders' valuations and provide worst-case (input-by-input) approximation guarantees. In contrast to previous work on this topic, we pursue good prior-free auctions with non-identical bidders. Prior-free auctions can approximate meaningful benchmarks for non-identical bidders only when ``sufficient qualitative information'' about the bidder asymmetry is publicly known. We consider digital goods auctions where there is a total ordering of the bidders that is known to the seller, where earlier bidders are in some sense thought to have higher valuations. We use the framework of Hartline and Roughgarden (STOC '08) to define an appropriate revenue benchmark: the maximum revenue that can be obtained from a bid vector using prices that are nonincreasing in the bidder ordering and bounded above by the second-highest bid. This monotone-price benchmark is always as large as the well-known fixed-price benchmark F$^{(2)}$, so designing prior-free auctions with good approximation guarantees is only harder. By design, an auction that approximates the monotone-price benchmark satisfies a very strong guarantee: it is, in particular, simultaneously near-optimal for essentially every Bayesian environment in which bidders' valuation distributions have nonincreasing monopoly prices, or in which the distribution of each bidder stochastically dominates that of the next. Of course, even if there is no distribution over bidders' valuations, such an auction still provides a quantifiable input-by-input performance guarantee. In this paper, we design a simple prior-free auction for digital goods with ordered bidders, the Random Price Restriction (RPR) auction. We prove that its expected revenue on every bid profile $b$ is $\Omega(M(b) / \log^*n)$, where $M$ denotes the monotone-price benchmark and $\log^*n$ denotes the number of times that the $\log_2$ operator can be applied to $n$ before the result drops below a fixed constant.", acknowledgement = ack-nhfb, } @InProceedings{Chawla:2012:LBB, author = "Shuchi Chawla and Nicole Immorlica and Brendan Lucier", title = "On the limits of black-box reductions in mechanism design", crossref = "ACM:2012:SPA", pages = "435--448", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214019", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We consider the problem of converting an arbitrary approximation algorithm for a single-parameter optimization problem into a computationally efficient truthful mechanism. We ask for reductions that are black-box, meaning that they require only oracle access to the given algorithm and in particular do not require explicit knowledge of the problem constraints. Such a reduction is known to be possible, for example, for the social welfare objective when the goal is to achieve Bayesian truthfulness and preserve social welfare in expectation. We show that a black-box reduction for the social welfare objective is not possible if the resulting mechanism is required to be truthful in expectation and to preserve the worst-case approximation ratio of the algorithm to within a subpolynomial factor. Further, we prove that for other objectives such as makespan, no black-box reduction is possible even if we only require Bayesian truthfulness and an average-case performance guarantee.", acknowledgement = ack-nhfb, } @InProceedings{Bei:2012:BFM, author = "Xiaohui Bei and Ning Chen and Nick Gravin and Pinyan Lu", title = "Budget feasible mechanism design: from prior-free to {Bayesian}", crossref = "ACM:2012:SPA", pages = "449--458", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214020", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Budget feasible mechanism design studies procurement combinatorial auctions in which the sellers have private costs to produce items, and the buyer (auctioneer) aims to maximize a social valuation function on subsets of items, under the budget constraint on the total payment. One of the most important questions in the field is ``which valuation domains admit truthful budget feasible mechanisms with 'small' approximations (compared to the social optimum)?'' Singer [35] showed that additive and submodular functions have a constant approximation mechanism. Recently, Dobzinski, Papadimitriou, and Singer [20] gave an $O(\log^2 n)$ approximation mechanism for subadditive functions; further, they remarked that: ``A fundamental question is whether, regardless of computational constraints, a constant-factor budget feasible mechanism exists for subadditive functions.'' In this paper, we address this question from two viewpoints: prior-free worst case analysis and Bayesian analysis, which are two standard approaches from computer science and economics, respectively. --- For the prior-free framework, we use a linear program (LP) that describes the fractional cover of the valuation function; the LP is also connected to the concept of approximate core in cooperative game theory. We provide a mechanism for subadditive functions whose approximation is $O(I)$, via the worst case integrality gap $I$ of this LP. This implies an $O(\log n)$-approximation for subadditive valuations, $O(1)$-approximation for XOS valuations, as well as for valuations having a constant integrality gap. XOS valuations are an important class of functions and lie between the submodular and the subadditive classes of valuations. We further give another polynomial time $O(\log n / (\log \log n))$ sub-logarithmic approximation mechanism for subadditive functions. Both of our mechanisms improve the best known approximation ratio $O(\log^2 n)$. --- For the Bayesian framework, we provide a constant approximation mechanism for all subadditive functions, using the above prior-free mechanism for XOS valuations as a subroutine. Our mechanism allows correlations in the distribution of private information and is universally truthful.", acknowledgement = ack-nhfb, } @InProceedings{Cai:2012:ACM, author = "Yang Cai and Constantinos Daskalakis and S. Matthew Weinberg", title = "An algorithmic characterization of multi-dimensional mechanisms", crossref = "ACM:2012:SPA", pages = "459--478", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214021", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We show that every feasible, Bayesian, multi-item multi-bidder mechanism for independent, additive bidders can be implemented as a mechanism that: (a) allocates every item independently of the other items; (b) for the allocation of each item it uses a strict ordering of all bidders' types; and allocates the item using a distribution over hierarchical mechanisms that iron this ordering into a non-strict ordering, and give the item uniformly at random to the bidders whose reported types dominate all other reported types according to the non-strict ordering. Combined with cyclic-monotonicity our results provide a characterization of feasible, Bayesian Incentive Compatible mechanisms in this setting. Our characterization is enabled by a new, constructive proof of Border's theorem [Border 1991], and a new generalization of this theorem to independent (but not necessarily identically distributed) bidders, improving upon the results of [Border 2007, Che--Kim--Mierendorf 2011]. For a single item and independent bidders, we show that every feasible reduced form auction can be implemented as a distribution over hierarchical mechanisms that are consistent with the same strict ordering of all bidders' types, which every mechanism in the support of the distribution irons to a non-strict ordering. We also give a polynomial-time algorithm for determining feasibility of a reduced form auction, or providing a separation hyperplane from the set of feasible reduced forms. To complete the picture, we provide polynomial-time algorithms to find and exactly sample from a distribution over hierarchical mechanisms consistent with a given feasible reduced form. All these results generalize to multi-item reduced form auctions for independent, additive bidders. Finally, for multiple items, additive bidders with hard demand constraints, and arbitrary value correlation across items or bidders, we give a proper generalization of Border's Theorem, and characterize feasible reduced form auctions as multi-commodity flows in related multi-commodity flow instances. We also show that our generalization holds for a broader class of feasibility constraints, including the intersection of any two matroids. As a corollary of our results we compute revenue-optimal, Bayesian Incentive Compatible (BIC) mechanisms in multi-item multi-bidder settings, when each bidder has arbitrarily correlated values over the items and additive valuations over bundles of items, and the bidders are independent. Our mechanisms run in time polynomial in the total number of bidder types (and {not} type profiles). This running time is polynomial in the number of bidders, but potentially exponential in the number of items. We improve the running time to polynomial in both the number of items and the number of bidders by using recent structural results on optimal BIC auctions in item-symmetric settings [Daskalakis--Weinberg 2011].", acknowledgement = ack-nhfb, } @InProceedings{Gal:2012:TBC, author = "Anna G{\'a}l and Kristoffer Arnsfelt Hansen and Michal Kouck{\'y} and Pavel Pudl{\'a}k and Emanuele Viola", title = "Tight bounds on computing error-correcting codes by bounded-depth circuits with arbitrary gates", crossref = "ACM:2012:SPA", pages = "479--494", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214023", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We bound the minimum number $w$ of wires needed to compute any (asymptotically good) error-correcting code $C: \{0, 1\}^{\Omega(n)} \to \{0, 1\}^n$ with minimum distance $\Omega(n)$, using unbounded fan-in circuits of depth $d$ with arbitrary gates. Our main results are: (1) If $d = 2$ then $w = \Theta(n({\log n/ \log \log n})^2)$. (2) If $d = 3$ then $w = \Theta(n \lg \lg n)$. (3) If $d = 2k$ or $d = 2k + 1$ for some integer $k \geq 2$ then $w = \Theta(n \lambda_k (n))$, where $\lambda_1(n) = \lceil \log n \rceil$, $\lambda_{i + 1}(n) = \lambda_i*(n)$, and the $*$ operation gives how many times one has to iterate the function $\lambda_i$ to reach a value at most $1$ from the argument $n$. (4) If $d = \log * n$ then $w = O(n)$. For depth $d = 2$, our $\Omega(n (\log n/\log \log n)^2)$ lower bound gives the largest known lower bound for computing any linear map. Using a result by Ishai, Kushilevitz, Ostrovsky, and Sahai (2008), we also obtain similar bounds for computing pairwise-independent hash functions. Our lower bounds are based on a superconcentrator-like condition that the graphs of circuits computing good codes must satisfy. This condition is provably intermediate between superconcentrators and their weakenings considered before.", acknowledgement = ack-nhfb, } @InProceedings{Chan:2012:TBM, author = "Siu Man Chan and Aaron Potechin", title = "Tight bounds for monotone switching networks via {Fourier} analysis", crossref = "ACM:2012:SPA", pages = "495--504", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214024", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We prove tight size bounds on monotone switching networks for the $k$-clique problem, and for an explicit monotone problem by analyzing the generation problem with a pyramid structure of height $h$. This gives alternative proofs of the separations of $m$-NC from $m$-P and of $m$-NC$^i$ from $m$-NC$^{i + 1}$, different from Raz--McKenzie (Combinatorica '99). The enumerative-combinatorial and Fourier analytic techniques in this work are very different from a large body of work on circuit depth lower bounds, and may be of independent interest.", acknowledgement = ack-nhfb, } @InProceedings{Braverman:2012:IIC, author = "Mark Braverman", title = "Interactive information complexity", crossref = "ACM:2012:SPA", pages = "505--524", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214025", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "The primary goal of this paper is to define and study the interactive information complexity of functions. Let $f(x,y)$ be a function, and suppose Alice is given $x$ and Bob is given $y$. Informally, the interactive information complexity ${\rm IC}(f)$ of $f$ is the least amount of information Alice and Bob need to reveal to each other to compute $f$. Previously, information complexity has been defined with respect to a prior distribution on the input pairs $(x,y)$. Our first goal is to give a definition that is independent of the prior distribution. We show that several possible definitions are essentially equivalent. We establish some basic properties of the interactive information complexity ${\rm IC}(f)$. In particular, we show that ${\rm IC}(f)$ is equal to the amortized (randomized) communication complexity of $f$. We also show a direct sum theorem for ${\rm IC}(f)$ and give the first general connection between information complexity and (non-amortized) communication complexity. This connection implies that a non-trivial exchange of information is required when solving problems that have non-trivial communication complexity. We explore the information complexity of two specific problems --- Equality and Disjointness. We show that only a constant amount of information needs to be exchanged when solving Equality with no errors, while solving Disjointness with a constant error probability requires the parties to reveal a linear amount of information to each other.", acknowledgement = ack-nhfb, } @InProceedings{Sherstov:2012:MCC, author = "Alexander A. Sherstov", title = "The multiparty communication complexity of set disjointness", crossref = "ACM:2012:SPA", pages = "525--548", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214026", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We study the set disjointness problem in the number-on-the-forehead model of multiparty communication.\par (i) We prove that $k$-party set disjointness has communication complexity $\Omega(n/4^k)^{1/4}$ in the randomized and nondeterministic models and $\Omega(n/4^k)^{1/8}$ in the Merlin--Arthur model. These lower bounds are close to tight. Previous lower bounds (2007-2008) for $k \geq 3$ parties were weaker than $\Omega(n/2^{k^3})^{1 / (k + 1)}$ in all three models.\par (ii) We prove that solving $\ell$ instances of set disjointness requires $\ell \cdot \Omega(n/4^k)^{1/4}$ bits of communication, even to achieve correctness probability exponentially close to $1/2$. This gives the first direct-product result for multiparty set disjointness, solving an open problem due to Beame, Pitassi, Segerlind, and Wigderson (2005).\par (iii) We construct a read-once $\{\wedge, \vee\}$-circuit of depth 3 with exponentially small discrepancy for up to $k \approx (1/2)\log n$ parties. This result is optimal with respect to depth and solves an open problem due to Beame and Huynh-Ngoc (FOCS '09), who gave a depth-$6$ construction. Applications to circuit complexity are given.", acknowledgement = ack-nhfb, } @InProceedings{Cheung:2012:FMR, author = "Ho Yee Cheung and Tsz Chiu Kwok and Lap Chi Lau", title = "Fast matrix rank algorithms and applications", crossref = "ACM:2012:SPA", pages = "549--562", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214028", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We consider the problem of computing the rank of an $m \times n$ matrix $A$ over a field. We present a randomized algorithm to find a set of $r = \rank(A)$ linearly independent columns in $O(|A| + r^w)$ field operations, where $|A|$ denotes the number of nonzero entries in $A$ and $w < 2.38$ is the matrix multiplication exponent. Previously the best known algorithm to find a set of $r$ linearly independent columns is by Gaussian elimination, with running time $O(m n r^w)$. Our algorithm is faster when $r < \max\{m, n\}$, for instance when the matrix is rectangular. We also consider the problem of computing the rank of a matrix dynamically, supporting the operations of rank one updates and additions and deletions of rows and columns. We present an algorithm that updates the rank in $O(m n)$ field operations. We show that these algorithms can be used to obtain faster algorithms for various problems in numerical linear algebra, combinatorial optimization and dynamic data structure.", acknowledgement = ack-nhfb, } @InProceedings{Hassanieh:2012:NOS, author = "Haitham Hassanieh and Piotr Indyk and Dina Katabi and Eric Price", title = "Nearly optimal sparse {Fourier} transform", crossref = "ACM:2012:SPA", pages = "563--578", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214029", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We consider the problem of computing the $k$-sparse approximation to the discrete Fourier transform of an $n$-dimensional signal. We show:\par (1) An $O(k \log n)$-time randomized algorithm for the case where the input signal has at most $k$ non-zero Fourier coefficients, and\par (2) An $O(k \log n \log (n/k))$-time randomized algorithm for general input signals.\par Both algorithms achieve $o(n \log n)$ time, and thus improve over the Fast Fourier Transform, for any $k = o(n)$. They are the first known algorithms that satisfy this property. Also, if one assumes that the Fast Fourier Transform is optimal, the algorithm for the exactly $k$-sparse case is optimal for any $k = n^{\Omega(1)}$.\par We complement our algorithmic results by showing that any algorithm for computing the sparse Fourier transform of a general signal must use at least $\Omega(k \log (n / k) / \log \log n)$ signal samples, even if it is allowed to perform adaptive sampling.", acknowledgement = ack-nhfb, } @InProceedings{Etessami:2012:PTA, author = "Kousha Etessami and Alistair Stewart and Mihalis Yannakakis", title = "Polynomial time algorithms for multi-type branching processes and stochastic context-free grammars", crossref = "ACM:2012:SPA", pages = "579--588", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214030", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We show that one can approximate the least fixed point solution for a multivariate system of monotone probabilistic polynomial equations in time polynomial in both the encoding size of the system of equations and in $\log (1 / \epsilon)$, where $\epsilon > 0$ is the desired additive error bound of the solution. (The model of computation is the standard Turing machine model.) We use this result to resolve several open problems regarding the computational complexity of computing key quantities associated with some classic and heavily studied stochastic processes, including multi-type branching processes and stochastic context-free grammars.", acknowledgement = ack-nhfb, } @InProceedings{Adamaszek:2012:OOB, author = "Anna Adamaszek and Artur Czumaj and Matthias Englert and Harald R{\"a}cke", title = "Optimal online buffer scheduling for block devices", crossref = "ACM:2012:SPA", pages = "589--598", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214031", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We introduce a buffer scheduling problem for block operation devices in an online setting. We consider a stream of items of different types to be processed by a block device. The block device can process all items of the same type in a single step. To improve the performance of the system a buffer of size $k$ is used to store items in order to reduce the number of operations required. Whenever the buffer becomes full a buffer scheduling strategy has to select one type and then a block operation on all elements with this type that are currently in the buffer is performed. The goal is to design a scheduling strategy that minimizes the number of block operations required. In this paper we consider the online version of this problem, where the buffer scheduling strategy must make decisions without knowing the future items that appear in the input stream. Our main result is the design of an $O(\log \log k)$-competitive online randomized buffer scheduling strategy. The bound is asymptotically tight. As a byproduct of our LP-based techniques, we obtain a randomized offline algorithm that approximates the optimal number of block operations to within a constant factor.", acknowledgement = ack-nhfb, } @InProceedings{Agrawal:2012:JHC, author = "Manindra Agrawal and Chandan Saha and Ramprasad Saptharishi and Nitin Saxena", title = "{Jacobian} hits circuits: hitting-sets, lower bounds for depth-{D} occur-$k$ formulas \& depth-$3$ transcendence degree-$k$ circuits", crossref = "ACM:2012:SPA", pages = "599--614", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214033", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We present a single common tool to strictly subsume all known cases of polynomial time blackbox polynomial identity testing (PIT), that have been hitherto solved using diverse tools and techniques, over fields of zero or large characteristic. In particular, we show that polynomial time hitting-set generators for identity testing of the two seemingly different and well studied models --- depth-3 circuits with bounded top fanin, and constant-depth constant-read multilinear formulas --- can be constructed using one common algebraic-geometry theme: Jacobian captures algebraic independence. By exploiting the Jacobian, we design the first efficient hitting-set generators for broad generalizations of the above-mentioned models, namely:\par (1) depth-3 $(\Omega \Pi \Omega)$ circuits with constant transcendence degree of the polynomials computed by the product gates (no bounded top fanin restriction), and\par (2) constant-depth constant-{\em occur\/} formulas (no multilinear restriction).\par Constant-{\rm occur} of a variable, as we define it, is a much more general concept than constant-read. Also, earlier work on the latter model assumed that the formula is multilinear. Thus, our work goes further beyond the related results obtained by Saxena \& Seshadhri (STOC 2011), Saraf \& Volkovich (STOC 2011), Anderson et al. (CCC 2011), Beecken et al. (ICALP 2011) and Grenet et al. (FSTTCS 2011), and brings them under one unifying technique.\par In addition, using the same Jacobian based approach, we prove exponential lower bounds for the immanant (which includes permanent and determinant) on the same depth-$3$ and depth-$4$ models for which we give efficient PIT algorithms. Our results reinforce the intimate connection between identity testing and lower bounds by exhibiting a concrete mathematical tool --- the Jacobian --- that is equally effective in solving both the problems on certain interesting and previously well-investigated (but not well understood) models of computation.", acknowledgement = ack-nhfb, } @InProceedings{Dvir:2012:SMB, author = "Zeev Dvir and Guillaume Malod and Sylvain Perifel and Amir Yehudayoff", title = "Separating multilinear branching programs and formulas", crossref = "ACM:2012:SPA", pages = "615--624", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214034", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "This work deals with the power of linear algebra in the context of multilinear computation. By linear algebra we mean algebraic branching programs (ABPs) which are known to be computationally equivalent to two basic tools in linear algebra: iterated matrix multiplication and the determinant. We compare the computational power of multilinear ABPs to that of multilinear arithmetic formulas, and prove a tight super-polynomial separation between the two models. Specifically, we describe an explicit $n$-variate polynomial $F$ that is computed by a linear-size multilinear ABP but every multilinear formula computing $F$ must be of size n$^{ \Omega(\log n)}$.", acknowledgement = ack-nhfb, } @InProceedings{Gupta:2012:RDM, author = "Ankit Gupta and Neeraj Kayal and Satya Lokam", title = "Reconstruction of depth-$4$ multilinear circuits with top fan-in $2$", crossref = "ACM:2012:SPA", pages = "625--642", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214035", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We present a randomized algorithm for reconstructing multilinear $\Sigma \Pi \Sigma \Pi (2)$ circuits, i.e., multilinear depth-$4$ circuits with fan-in $2$ at the top $+$ gate. The algorithm is given blackbox access to a polynomial $f \in F[x_1,\ldots{},x_n]$ computable by a multilinear $\Sigma \Pi \Sigma \Pi (2)$ circuit of size $s$ and outputs an equivalent multilinear $\Sigma \Pi \Sigma \Pi (2)$ circuit, runs in time $\poly(n,s)$, and works over any field $F$. This is the first reconstruction result for any model of depth-$4$ arithmetic circuits. Prior to our work, reconstruction results for bounded depth circuits were known only for depth-$2$ arithmetic circuits (Klivans \& Spielman, STOC 2001), $\Sigma \Pi \Sigma (2)$ circuits (depth-$3$ arithmetic circuits with top fan-in $2$) (Shpilka, STOC 2007), and $\Sigma \Pi \Sigma (k)$ with $k = O(1)$ (Karnin \& Shpilka, CCC 2009). Moreover, the running times of these algorithms have a polynomial dependence on $4|F|$ and hence do not work for infinite fields such as $Q$. Our techniques are quite different from the previous ones for depth-$3$ reconstruction and rely on a polynomial operator introduced by Karnin et al. (STOC 2010) and Saraf \& Volkovich (STOC 2011) for devising blackbox identity tests for multilinear $\Sigma \Pi \Sigma \Pi (k)$ circuits. Some other ingredients of our algorithm include the classical multivariate blackbox factoring algorithm by Kaltofen \& Trager (FOCS 1988) and an average-case algorithm for reconstructing $\Sigma \Pi \Sigma (2)$ circuits by Kayal.", acknowledgement = ack-nhfb, } @InProceedings{Kayal:2012:APP, author = "Neeraj Kayal", title = "Affine projections of polynomials: extended abstract", crossref = "ACM:2012:SPA", pages = "643--662", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214036", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "An $m$-variate polynomial $f$ is said to be an affine projection of some $n$-variate polynomial $g$ if there exists an $n m$ matrix $A$ and an $n$-dimensional vector $b$ such that $f(x) = g(Ax + b)$. In other words, if $f$ can be obtained by replacing each variable of $g$ by an affine combination of the variables occurring in $f$, then it is said to be an affine projection of $g$. Some well known problems (such as the determinant versus permanent and matrix multiplication for example) are instances of this problem. Given $f$ and $g$ can we determine whether $f$ is an affine projection of $g$? The intention of this paper is to understand the complexity of the corresponding computational problem: given polynomials $f$ and $g$ find $A$ and $b$ such that $f = g(A x + b)$, if such an $(A b)$ exists. We first show that this is an NP-hard problem. We then focus our attention on instances where $g$ is a member of some fixed, well known family of polynomials so that the input consists only of the polynomial $f(x)$ having $m$ variables and degree $d$. We consider the situation where $f(x)$ is given to us as a blackbox (i.e. for any point $aFm$ we can query the blackbox and obtain $f(a)$ in one step) and devise randomized algorithms with running time $\poly(m n d)$ in the following special cases. Firstly where $g$ is the Permanent (respectively the Determinant) of an $n \times n$ matrix and $A$ is of rank $n^2$. Secondly where $g$ is the sum of powers polynomial (respectively the sum of products polynomial), and $A$ is a random matrix of the appropriate dimensions (also $d$ should not be too small).", acknowledgement = ack-nhfb, } @InProceedings{Bartal:2012:TSP, author = "Yair Bartal and Lee-Ad Gottlieb and Robert Krauthgamer", title = "The traveling salesman problem: low-dimensionality implies a polynomial time approximation scheme", crossref = "ACM:2012:SPA", pages = "663--672", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214038", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a $(1 + \mu)$-approximation to the optimal tour, for any fixed $\mu > 0$, in TSP instances that form an arbitrary metric space with bounded intrinsic dimension. The celebrated results of Arora [Aro98] and Mitchell [Mit99] prove that the above result holds in the special case of TSP in a fixed-dimensional Euclidean space. Thus, our algorithm demonstrates that the algorithmic tractability of metric TSP depends on the dimensionality of the space and not on its specific geometry. This result resolves a problem that has been open since the quasi-polynomial time algorithm of Talwar [Tal04].", acknowledgement = ack-nhfb, } @InProceedings{Chuzhoy:2012:VSS, author = "Julia Chuzhoy", title = "On vertex sparsifiers with {Steiner} nodes", crossref = "ACM:2012:SPA", pages = "673--688", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214039", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Given an undirected graph $G = (V, E)$ with edge capacities $c_e \geq 1$ for $e \in E$ and a subset $T$ of $k$ vertices called terminals, we say that a graph $H$ is a quality-$q$ cut sparsifier for $G$ iff $T \subseteq V(H)$, and for any partition $(A, B)$ of $T$, the values of the minimum cuts separating $A$ and $B$ in graphs $G$ and $H$ are within a factor $q$ from each other. We say that $H$ is a quality-$q$ flow sparsifier for $G$ iff $T \subseteq V(H)$, and for any set $D$ of demands over the terminals, the values of the minimum edge congestion incurred by fractionally routing the demands in $D$ in graphs $G$ and $H$ are within a factor $q$ from each other.\par So far vertex sparsifiers have been studied in a restricted setting where the sparsifier $H$ is not allowed to contain any non-terminal vertices, that is $V(H) = {\cal T}$. For this setting, efficient algorithms are known for constructing quality-$O(\log k/\log \log k)$ cut and flow vertex sparsifiers, as well as a lower bound of $\tilde{\Omega}(\sqrt{\log k})$ on the quality of any flow or cut sparsifier.\par We study flow and cut sparsifiers in the more general setting where Steiner vertices are allowed, that is, we no longer require that $V(H) = {\cal T}$. We show algorithms to construct constant-quality cut sparsifiers of size $O(C^3)$ in time $\poly(n) \cdot 2^C$, and constant-quality flow sparsifiers of size $C^{O(\log \log C)}$ in time $n^{O(\log C)} \cdot 2^C$, where $C$ is the total capacity of the edges incident on the terminals.", acknowledgement = ack-nhfb, } @InProceedings{Chalermsook:2012:AAH, author = "Parinya Chalermsook and Julia Chuzhoy and Alina Ene and Shi Li", title = "Approximation algorithms and hardness of integral concurrent flow", crossref = "ACM:2012:SPA", pages = "689--708", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214040", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We study an integral counterpart of the classical Maximum Concurrent Flow problem, that we call Integral Concurrent Flow (ICF). In the basic version of this problem (basic-ICF), we are given an undirected $n$-vertex graph $G$ with edge capacities $c(e)$, a subset $T$ of vertices called terminals, and a demand $D(t,t')$ for every pair $(t,t')$ of the terminals. The goal is to find a maximum value $\lambda$, and a collection $P$ of paths, such that every pair $(t,t')$ of terminals is connected by $\lfloor \lambda \cdot D(t,t') \rfloor$ paths in $P$, and the number of paths containing any edge $e$ is at most $c(e)$. We show an algorithm that achieves a $\poly \log n$-approximation for basic-ICF, while violating the edge capacities by only a constant factor. We complement this result by proving that no efficient algorithm can achieve a factor $\alpha$-approximation with congestion $c$ for any values $\alpha$, $c$ satisfying $\alpha \cdot c = O(\log \log n / \log \log \log n)$, unless NP $\subseteq$ ZPTIME(n$^{\poly \log n}$). We then turn to study the more general group version of the problem (group = ICF), in which we are given a collection $(S_1, T_1), \ldots{}, (S_k, T_k)$ of pairs of vertex subsets, and for each $1 \leq $i$ \leq k$, a demand D$_i$ is specified. The goal is to find a maximum value $\lambda$ and a collection $P$ of paths, such that for each $i$, at least $\lfloor \lambda \cdot D_i \rfloor$ paths connect the vertices of $S_i$ to the vertices of $T_i$, while respecting the edge capacities. We show that for any $1 \leq $c$ \leq O(\log \log n)$, no efficient algorithm can achieve a factor $O(n^{1/(2 2c + 3)})$-approximation with congestion $c$ for the problem, unless NP $\subseteq$ DTIME($n^{O(\log \log n)}$). On the other hand, we show an efficient randomized algorithm that finds a $\poly \log n$-approximate solution with a constant congestion, if we are guaranteed that the optimal solution contains at least $D \geq $k$ \poly \log n$ paths connecting every pair (S$_i$, T$_i$).", acknowledgement = ack-nhfb, } @InProceedings{Daskalakis:2012:LPB, author = "Constantinos Daskalakis and Ilias Diakonikolas and Rocco A. Servedio", title = "Learning {Poisson} binomial distributions", crossref = "ACM:2012:SPA", pages = "709--728", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214042", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We consider a basic problem in unsupervised learning: learning an unknown Poisson Binomial Distribution. A Poisson Binomial Distribution (PBD) over $\{0, 1,\ldots{}, n\}$ is the distribution of a sum of $n$ independent Bernoulli random variables which may have arbitrary, potentially non-equal, expectations. These distributions were first studied by S. Poisson in 1837 and are a natural $n$-parameter generalization of the familiar Binomial Distribution. Surprisingly, prior to our work this basic learning problem was poorly understood, and known results for it were far from optimal. We essentially settle the complexity of the learning problem for this basic class of distributions. As our main result we give a highly efficient algorithm which learns to $\epsilon$-accuracy using $O(1 / \epsilon^3)$ samples independent of $n$. The running time of the algorithm is quasilinear in the size of its input data, i.e. $\tilde{O}(\log (n)/ \epsilon^3)$ bit-operations (observe that each draw from the distribution is a $\log(n)$-bit string). This is nearly optimal since any algorithm must use $\Omega(1 / \epsilon^2)$ samples. We also give positive and negative results for some extensions of this learning problem.", acknowledgement = ack-nhfb, } @InProceedings{De:2012:NOS, author = "Anindya De and Ilias Diakonikolas and Vitaly Feldman and Rocco A. Servedio", title = "Nearly optimal solutions for the chow parameters problem and low-weight approximation of halfspaces", crossref = "ACM:2012:SPA", pages = "729--746", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214043", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "The Chow parameters of a Boolean function $f: \{-1, 1\}^n \to \{-1, 1\}$ are its $n + 1$ degree-$0$ and degree-$1$ Fourier coefficients. It has been known since 1961 [Cho61, Tan61] that the (exact values of the) Chow parameters of any linear threshold function $f$ uniquely specify $f$ within the space of all Boolean functions, but until recently [OS11] nothing was known about efficient algorithms for reconstructing $f$ (exactly or approximately) from exact or approximate values of its Chow parameters. We refer to this reconstruction problem as the Chow Parameters Problem. Our main result is a new algorithm for the Chow Parameters Problem which, given (sufficiently accurate approximations to) the Chow parameters of any linear threshold function f, runs in time $\tilde{O}(n^2) o(1/ \epsilon)^{O(\log 2 (1 / \epsilon))}$ and with high probability outputs a representation of an LTF $f'$ that is $\epsilon$-close to $f$. The only previous algorithm [OS11] had running time $\poly(n) \cdot 2^{2 \tilde{O}(1 / \epsilon 2)}$. As a byproduct of our approach, we show that for any linear threshold function $f$ over ${-1,1}^n$, there is a linear threshold function $f'$ which is $\epsilon$-close to $f$ and has all weights that are integers at most $\sqrt n o(1 / \epsilon)^{O(\log 2 (1 / \epsilon))}$. This significantly improves the best previous result of [Serv09] which gave a $\poly(n) o 2^{O(1 / \epsilon 2/3)}$ weight bound, and is close to the known lower bound of $\max\{\sqrt n, (1 / \epsilon)^{\Omega(\log \log (1 / \epsilon))}\}$ [Gol06,Serv07]. Our techniques also yield improved algorithms for related problems in learning theory. In addition to being significantly stronger than previous work, our results are obtained using conceptually simpler proofs. The two main ingredients underlying our results are (1) a new structural result showing that for $f$ any linear threshold function and g any bounded function, if the Chow parameters of $f$ are close to the Chow parameters of $g$ then $f$ is close to g; (2) a new boosting-like algorithm that given approximations to the Chow parameters of a linear threshold function outputs a bounded function whose Chow parameters are close to those of $f$.", } @InProceedings{Sherstov:2012:MPR, author = "Alexander A. Sherstov", title = "Making polynomials robust to noise", crossref = "ACM:2012:SPA", pages = "747--758", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214044", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "A basic question in any computational model is how to reliably compute a given function when the inputs or intermediate computations are subject to noise at a constant rate. Ideally, one would like to use at most a constant factor more resources compared to the noise-free case. This question has been studied for decision trees, circuits, automata, data structures, broadcast networks, communication protocols, and other models. Buhrman et al. (2003) posed the noisy computation problem for real polynomials. We give a complete solution to this problem. For any polynomial $p : \{0, 1\}^n \to [-1, 1]$, we construct a polynomial $p_{\rm robust}: R^n \to R$ of degree $O(\deg p + \log(1 / \epsilon))$ that $\epsilon$-approximates $p$ and is robust to noise in the inputs: $|p(x) - p_{\rm robust} (x + \delta)| < \epsilon$ for all $x \in \{0, 1\}^n$ and all $\delta \in [-1/3, 1/3]^n$. This result is optimal with respect to all parameters. We construct $p_{\rm robust}$ explicitly for each $p$. Previously, it was open to give such a construction even for $p = x_1 \oplus x_2 \oplus \ldots{} \oplus x_n$ (Buhrman et al., 2003). The proof contributes a technique of independent interest, which allows one to force partial cancellation of error terms in a polynomial.", acknowledgement = ack-nhfb, } @InProceedings{Goyal:2012:CCN, author = "Sanjeev Goyal and Michael Kearns", title = "Competitive contagion in networks", crossref = "ACM:2012:SPA", pages = "759--774", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214046", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We develop a game-theoretic framework for the study of competition between firms who have budgets to ``seed'' the initial adoption of their products by consumers located in a social network. The payoffs to the firms are the eventual number of adoptions of their product through a competitive stochastic diffusion process in the network. This framework yields a rich class of competitive strategies, which depend in subtle ways on the stochastic dynamics of adoption, the relative budgets of the players, and the underlying structure of the social network. We identify a general property of the adoption dynamics --- namely, decreasing returns to local adoption --- for which the inefficiency of resource use at equilibrium (the Price of Anarchy) is uniformly bounded above, across all networks. We also show that if this property is violated the Price of Anarchy can be unbounded, thus yielding sharp threshold behavior for a broad class of dynamics. We also introduce a new notion, the Budget Multiplier, that measures the extent that imbalances in player budgets can be amplified at equilibrium. We again identify a general property of the adoption dynamics --- namely, proportional local adoption between competitors --- for which the (pure strategy) Budget Multiplier is uniformly bounded above, across all networks. We show that a violation of this property can lead to unbounded Budget Multiplier, again yielding sharp threshold behavior for a broad class of dynamics.", acknowledgement = ack-nhfb, } @InProceedings{Cebrian:2012:FRB, author = "Manuel Cebrian and Lorenzo Coviello and Andrea Vattani and Panagiotis Voulgaris", title = "Finding red balloons with split contracts: robustness to individuals' selfishness", crossref = "ACM:2012:SPA", pages = "775--788", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214047", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "The present work deals with the problem of information acquisition in a strategic networked environment. To study this problem, Kleinberg and Raghavan (FOCS 2005) introduced the model of {\em query incentive networks}, where the root of a binomial branching process wishes to retrieve an information --- known by each node independently with probability 1/n --- by investing as little as possible. The authors considered {\em fixed-payment contracts\/} in which every node strategically chooses an amount to offer its children paid upon information retrieval to convince them to seek the information in their subtrees. Kleinberg and Raghavan discovered that the investment needed at the root exhibits an unexpected threshold behavior that depends on the branching parameter b. For b > 2, the investment is linear in the expected distance to the closest information (logarithmic in $n$, the rarity of the information), while, for $1 < b < 2$, it becomes exponential in the same distance (i.e., polynomial in $n$). Arcaute et al. (EC 2007) later observed the same threshold behavior for arbitrary Galton--Watson branching processes.\par The DARPA Network Challenge --- retrieving the locations of ten balloons placed at undisclosed positions in the US --- has recently brought practical attention to the problems of social mobilization and information acquisition in a networked environment. The MIT Media Laboratory team won the challenge by acting as the root of a query incentive network that unfolded all over the world. However, rather than adopting a {\em fixed-payment strategy}, the team implemented a different incentive scheme based on {\em $1/2$-split contracts}. Under such incentive scheme, a node $u$ who does not possess the information can recruit a friend $v$ through a contract stipulating that if the information is found in the subtree rooted at $v$, then $v$ has to give half of her own reward back to $u$.\par Motivated by its empirical success, we present a comprehensive theoretical study of this scheme in the game theoretical setting of query incentive networks. Our main result is that split contracts are robust --- as opposed to fixed-payment contracts --- to nodes' selfishness. Surprisingly, when nodes determine the splits to offer their children based on the contracts received from their recruiters, the threshold behavior observed in the previous work vanishes, and an investment linear in the expected distance to the closest information is sufficient to retrieve the information in {\em any arbitrary\/} Galton--Watson process with $b > 1$. Finally, while previous analyses considered the parameters of the branching process as constants, we are able to characterize the rate of the investment in terms of the branching process and the desired probability of success. This allows us to show improvements even in other special cases.", acknowledgement = ack-nhfb, } @InProceedings{Brandt:2012:AOD, author = "Christina Brandt and Nicole Immorlica and Gautam Kamath and Robert Kleinberg", title = "An analysis of one-dimensional {Schelling} segregation", crossref = "ACM:2012:SPA", pages = "789--804", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214048", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We analyze the Schelling model of segregation in which a society of $n$ individuals live in a ring. Each individual is one of two races and is only satisfied with his location so long as at least half his 2w nearest neighbors are of the same race as him. In the dynamics, randomly-chosen unhappy individuals successively swap locations. We consider the average size of monochromatic neighborhoods in the final stable state. Our analysis is the first rigorous analysis of the Schelling dynamics. We note that, in contrast to prior approximate analyses, the final state is nearly integrated: the average size of monochromatic neighborhoods is independent of $n$ and polynomial in w.", acknowledgement = ack-nhfb, } @InProceedings{Applebaum:2012:PGL, author = "Benny Applebaum", title = "Pseudorandom generators with long stretch and low locality from random local one-way functions", crossref = "ACM:2012:SPA", pages = "805--816", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214050", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We continue the study of {\em locally-computable\/} pseudorandom generators (PRG) $G : \{0, 1\}^n \to \{0, 1\}^m$ that each of their outputs depend on a small number of $d$ input bits. While it is known that such generators are likely to exist for the case of small sub-linear stretch $m = n + n^{1 - \delta}$, it is less clear whether achieving larger stretch such as $m = n + \Omega(n)$, or even $m = n^{1 + \delta}$ is possible. The existence of such PRGs, which was posed as an open question in previous works, has recently gained an additional motivation due to several interesting applications.\par We make progress towards resolving this question by obtaining several local constructions based on the one-wayness of ``random'' local functions --- a variant of an assumption made by Goldreich (ECCC 2000). Specifically, we construct collections of PRGs with the following parameters:\par 1. Linear stretch $m = n + \Omega(n)$ and constant locality $d = O(1)$.\par 2. Polynomial stretch $m = n^{1 + \delta}$ and {\em any\/} (arbitrarily slowly growing) super-constant locality $d = \omega(1)$, e.g., $\log^*n$.\par 3. Polynomial stretch $m = n^{1 + \delta}$, constant locality $d = O(1)$, and inverse polynomial distinguishing advantage (as opposed to the standard case of $n^{-\omega(1)}$).\par As an additional contribution, we show that our constructions give rise to strong inapproximability results for the densest-subgraph problem in $d$-uniform hypergraphs for constant $d$. This allows us to improve the previous bounds of Feige (STOC 2002) and Khot (FOCS 2004) from constant inapproximability factor to $n^\epsilon$-inapproximability, at the expense of relying on stronger assumptions.", acknowledgement = ack-nhfb, } @InProceedings{Vadhan:2012:CPS, author = "Salil Vadhan and Colin Jia Zheng", title = "Characterizing pseudoentropy and simplifying pseudorandom generator constructions", crossref = "ACM:2012:SPA", pages = "817--836", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214051", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We provide a characterization of pseudoentropy in terms of hardness of sampling: Let $(X, B)$ be jointly distributed random variables such that $B$ takes values in a polynomial-sized set. We show that $B$ is computationally indistinguishable from a random variable of higher Shannon entropy given $X$ if and only if there is no probabilistic polynomial-time $S$ such that $(X, S(X))$ has small KL divergence from $(X, B)$. This can be viewed as an analogue of the Impagliazzo Hardcore Theorem (FOCS '95) for Shannon entropy (rather than min-entropy).\par Using this characterization, we show that if $f$ is a one-way function, then $(f(U_n), U_n)$ has ``next-bit pseudoentropy'' at least $n + \log n$, establishing a conjecture of Haitner, Reingold, and Vadhan (STOC '10). Plugging this into the construction of Haitner et al., this yields a simpler construction of pseudorandom generators from one-way functions. In particular, the construction only performs hashing once, and only needs the hash functions that are randomness extractors (e.g. universal hash functions) rather than needing them to support ``local list-decoding'' (as in the Goldreich--Levin hardcore predicate, STOC '89).\par With an additional idea, we also show how to improve the seed length of the pseudorandom generator to $\tilde{O}(n^3)$, compared to $\tilde{O}(n^4)$ in the construction of Haitner et al.", acknowledgement = ack-nhfb, } @InProceedings{Li:2012:DEN, author = "Xin Li", title = "Design extractors, non-malleable condensers and privacy amplification", crossref = "ACM:2012:SPA", pages = "837--854", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214052", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We introduce a new combinatorial object, called a design extractor, that has both the properties of a design and an extractor. We give efficient constructions of such objects and show that they can be used in several applications.\par 1. {\bf Improving the output length of known non-malleable extractors.} Non-malleable extractors were introduced in [DW09] to study the problem of privacy amplification with an active adversary. Currently, only two explicit constructions are known [DLWZ11, CRS11]. Both constructions work for $n$ bit sources with min-entropy $k > n / 2$. However, in both constructions the output length is smaller than the seed length, while the probabilistic method shows that to achieve error $\epsilon$, one can use $O(\log n + \log (1 / \epsilon))$ bits to extract up to $k/2$ output bits. In this paper, we use our design extractor to give an explicit non-malleable extractor for min-entropy $k > n / 2$, that has seed length $O(\log n + \log (1 / \epsilon))$ and output length $\Omega(k)$.\par 2. {\bf Non-malleable condensers.} We introduce and define the notion of a {\em non-malleable condenser}. A non-malleable condenser is a generalization and relaxation of a non-malleable extractor. We show that similar as extractors and condensers, non-malleable condensers can be used to construct non-malleable extractors. We then show that our design extractor already gives a non-malleable condenser for min-entropy $k > n / 2$, with error $\epsilon$ and seed length $O(\log (1 / \epsilon))$.\par 3. {\bf A new optimal protocol for privacy amplification.} More surprisingly, we show that non-malleable condensers themselves give optimal privacy amplification protocols with an active adversary. In fact, the non-malleable condensers used in these protocols are much weaker compared to non-malleable extractors, in the sense that the entropy rate of the condenser's output does not need to increase at all. This suggests that one promising next step to achieve better privacy amplification protocols may be to construct non-malleable condensers for smaller min-entropy. As a by-product, we also obtain a new explicit $2$-round privacy amplification protocol with optimal entropy loss and optimal communication complexity for min-entropy $k > n / 2$, without using non-malleable extractors.", acknowledgement = ack-nhfb, } @InProceedings{Chuzhoy:2012:RUG, author = "Julia Chuzhoy", title = "Routing in undirected graphs with constant congestion", crossref = "ACM:2012:SPA", pages = "855--874", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214054", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Given an undirected graph $G = (V,E)$, a collection $(s_1, t_1)$, \ldots{}, $(s_k, t_k)$ of $k$ demand pairs, and an integer $c$, the goal in the Edge Disjoint Paths with Congestion problem is to connect maximum possible number of the demand pairs by paths, so that the maximum load on any edge (called edge congestion) does not exceed $c$. We show an efficient randomized algorithm that routes $\Omega({\rm OPT} / \poly \log k)$ demand pairs with congestion at most $14$, where OPT is the maximum number of pairs that can be simultaneously routed on edge-disjoint paths. The best previous algorithm that routed $\Omega({\rm OPT} / \poly \log n)$ pairs required congestion $\poly(\log \log n)$, and for the setting where the maximum allowed congestion is bounded by a constant $c$, the best previous algorithms could only guarantee the routing of OPT / $n^{O(1/c)}$ pairs. We also introduce a new type of vertex sparsifiers that we call integral flow sparsifiers, which approximately preserve both fractional and integral routings, and show an algorithm to construct such sparsifiers.", acknowledgement = ack-nhfb, } @InProceedings{An:2012:ICA, author = "Hyung-Chan An and Robert Kleinberg and David B. Shmoys", title = "Improving {Christofides}' algorithm for the $s$-$t$ path {TSP}", crossref = "ACM:2012:SPA", pages = "875--886", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214055", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We present a deterministic $(1 + \sqrt 5/2)$-approximation algorithm for the $s$-$t$ path TSP for an arbitrary metric. Given a symmetric metric cost on $n$ vertices including two prespecified endpoints, the problem is to find a shortest Hamiltonian path between the two endpoints; Hoogeveen showed that the natural variant of Christofides' algorithm is a $5/3$-approximation algorithm for this problem, and this asymptotically tight bound in fact had been the best approximation ratio known until now. We modify this algorithm so that it chooses the initial spanning tree based on an optimal solution to the Held--Karp relaxation rather than a minimum spanning tree; we prove this simple but crucial modification leads to an improved approximation ratio, surpassing the 20-year-old barrier set by the natural Christofides' algorithm variant. Our algorithm also proves an upper bound of $1 + \sqrt 5/2$ on the integrality gap of the path-variant Held--Karp relaxation. The techniques devised in this paper can be applied to other optimization problems as well: these applications include improved approximation algorithms and improved LP integrality gap upper bounds for the prize-collecting $s$-$t$ path problem and the unit-weight graphical metric $s$-$t$ path TSP.", acknowledgement = ack-nhfb, } @InProceedings{Williams:2012:MMF, author = "Virginia Vassilevska Williams", title = "Multiplying matrices faster than {Coppersmith--Winograd}", crossref = "ACM:2012:SPA", pages = "887--898", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214056", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We develop an automated approach for designing matrix multiplication algorithms based on constructions similar to the Coppersmith--Winograd construction. Using this approach we obtain a new improved bound on the matrix multiplication exponent $\omega < 2.3727$.", acknowledgement = ack-nhfb, keywords = "fast matrix multiplication", } @InProceedings{Coja-Oglan:2012:CKN, author = "Amin Coja-Oglan and Konstantinos Panagiotou", title = "Catching the {$k$-NAESAT} threshold", crossref = "ACM:2012:SPA", pages = "899--908", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214058", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "The best current estimates of the thresholds for the existence of solutions in random constraint satisfaction problems ('CSPs') mostly derive from the first and the second moment method. Yet apart from a very few exceptional cases these methods do not quite yield matching upper and lower bounds. According to deep but non-rigorous arguments from statistical mechanics, this discrepancy is due to a change in the geometry of the set of solutions called condensation that occurs shortly before the actual threshold for the existence of solutions (Krzakala, Montanari, Ricci-Tersenghi, Semerjian, Zdeborova: PNAS~2007). To cope with condensation, physicists have developed a sophisticated but non-rigorous formalism called Survey Propagation (Mezard, Parisi, Zecchina: Science 2002). This formalism yields precise conjectures on the threshold values of many random CSPs. Here we develop a new Survey Propagation inspired second moment method for the random $k$-NAESAT problem, which is one of the standard benchmark problems in the theory of random CSPs. This new technique allows us to overcome the barrier posed by condensation rigorously. We prove that the threshold for the existence of solutions in random $k$-NAESAT is $2^{k-1} \ln 2 - (\ln / 2 2 + 1/4) + \epsilon_k$, where $|\epsilon_k| \leq 2^{-(1 -o k(1))k}$, thereby verifying the statistical mechanics conjecture for this problem.", acknowledgement = ack-nhfb, } @InProceedings{Cai:2012:CCC, author = "Jin-Yi Cai and Xi Chen", title = "Complexity of counting {CSP} with complex weights", crossref = "ACM:2012:SPA", pages = "909--920", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214059", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We give a complexity dichotomy theorem for the counting constraint satisfaction problem (\#CSP in short) with algebraic complex weights. To this end, we give three conditions for its tractability. Let $F$ be any finite set of complex-valued functions. We show that \#CSP($F$) is solvable in polynomial time if all three conditions are satisfied; and is \#P-hard otherwise. Our dichotomy theorem generalizes a long series of important results on counting problems: (a) the problem of counting graph homomorphisms is the special case when $F$ has a single symmetric binary function; (b) the problem of counting directed graph homomorphisms is the special case when $F$ has a single but not-necessarily-symmetric binary function; and (c) the unweighted form of \#CSP is when all functions in $F$ take values in $\{0, 1\}$.", acknowledgement = ack-nhfb, } @InProceedings{Molloy:2012:FTK, author = "Michael Molloy", title = "The freezing threshold for $k$-colourings of a random graph", crossref = "ACM:2012:SPA", pages = "921--930", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214060", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We rigorously determine the exact freezing threshold, $r_k^f$, for $k$-colourings of a random graph. We prove that for random graphs with density above $r_k^f$, almost every colouring is such that a linear number of variables are {\em frozen}, meaning that their colours cannot be changed by a sequence of alterations whereby we change the colours of $o(n)$ vertices at a time, always obtaining another proper colouring. When the density is below $r_k^f$, then almost every colouring has at most $o(n)$ frozen variables. This confirms hypotheses made using the non-rigorous cavity method.\par It has been hypothesized that the freezing threshold is the cause of the ``algorithmic barrier'', the long observed phenomenon that when the edge-density of a random graph exceeds $(1/2) k \ln k(1 + o_k(1))$, no algorithms are known to find $k$-colourings, despite the fact that this density is only half the $k$-colourability threshold.\par We also show that $r_k^f$ is the threshold of a strong form of reconstruction for $k$-colourings of the Galton--Watson tree, and of the graphical model.", acknowledgement = ack-nhfb, } @InProceedings{Barto:2012:RSC, author = "Libor Barto and Marcin Kozik", title = "Robust satisfiability of constraint satisfaction problems", crossref = "ACM:2012:SPA", pages = "931--940", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214061", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "An algorithm for a constraint satisfaction problem is called robust if it outputs an assignment satisfying at least $(1 - g(\epsilon))$-fraction of the constraints given a $(1 - \epsilon)$-satisfiable instance, where $g(\epsilon) \to 0$ as $\epsilon \to 0$, $g(0) = 0$. Guruswami and Zhou conjectured a characterization of constraint languages for which the corresponding constraint satisfaction problem admits an efficient robust algorithm. This paper confirms their conjecture.", acknowledgement = ack-nhfb, } @InProceedings{Woodruff:2012:TBD, author = "David P. Woodruff and Qin Zhang", title = "Tight bounds for distributed functional monitoring", crossref = "ACM:2012:SPA", pages = "941--960", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214063", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We resolve several fundamental questions in the area of distributed functional monitoring, initiated by Cormode, Muthukrishnan, and Yi (SODA, 2008), and receiving recent attention. In this model there are $k$ sites each tracking their input streams and communicating with a central coordinator. The coordinator's task is to continuously maintain an approximate output to a function computed over the union of the $k$ streams. The goal is to minimize the number of bits communicated. Let the $p$-th frequency moment be defined as $F_p = \sum_i f_i^p$, where $f_i$ is the frequency of element $i$. We show the randomized communication complexity of estimating the number of distinct elements (that is, $F_0$) up to a $1 + \epsilon$ factor is $\Omega(k / \epsilon^2)$, improving upon the previous $\Omega(k + 1/ \epsilon^2)$ bound and matching known upper bounds. For $F_p$, $p > 1$, we improve the previous $\Omega(k + 1/ \epsilon^2)$ communication bound to $\Omega(k^{p - 1} / \epsilon^2)$. We obtain similar improvements for heavy hitters, empirical entropy, and other problems. Our lower bounds are the first of any kind in distributed functional monitoring to depend on the product of $k$ and $1 / \epsilon^2$. Moreover, the lower bounds are for the static version of the distributed functional monitoring model where the coordinator only needs to compute the function at the time when all $k$ input streams end; surprisingly they almost match what is achievable in the (dynamic version of) distributed functional monitoring model where the coordinator needs to keep track of the function continuously at any time step. We also show that we can estimate $F_p$, for any $p > 1$, using $O(k^{p - 1} \poly(\epsilon^{-1}))$ communication. This drastically improves upon the previous $O(k^{2 p + 1} N^{1 - 2/p} \poly(\epsilon^{-1}))$ bound of Cormode, Muthukrishnan, and Yi for general $p$, and their $O(k^2 / \epsilon + k^{1.5} / \epsilon^3)$ bound for $p = 2$. For $p = 2$, our bound resolves their main open question. Our lower bounds are based on new direct sum theorems for approximate majority, and yield improvements to classical problems in the standard data stream model. First, we improve the known lower bound for estimating $F_p$, $p > 2$, in $t$ passes from $\Omega(n^{1 - 2 / p} /(\epsilon^{2 / p} t))$ to $\Omega(n^{1 - 2 / p} /(\epsilon^{4 / p} t))$, giving the first bound that matches what we expect when $p = 2$ for any constant number of passes. Second, we give the first lower bound for estimating $F_0$ in $t$ passes with $\Omega(1 / (\epsilon^2 t))$ bits of space that does not use the hardness of the gap-Hamming problem.", acknowledgement = ack-nhfb, } @InProceedings{Censor-Hillel:2012:GCP, author = "Keren Censor-Hillel and Bernhard Haeupler and Jonathan Kelner and Petar Maymounkov", title = "Global computation in a poorly connected world: fast rumor spreading with no dependence on conductance", crossref = "ACM:2012:SPA", pages = "961--970", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214064", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "In this paper, we study the question of how efficiently a collection of interconnected nodes can perform a global computation in the GOSSIP model of communication. In this model, nodes do not know the global topology of the network, and they may only initiate contact with a single neighbor in each round. This model contrasts with the much less restrictive LOCAL model, where a node may simultaneously communicate with all of its neighbors in a single round. A basic question in this setting is how many rounds of communication are required for the information dissemination problem, in which each node has some piece of information and is required to collect all others. In the LOCAL model, this is quite simple: each node broadcasts all of its information in each round, and the number of rounds required will be equal to the diameter of the underlying communication graph. In the GOSSIP model, each node must independently choose a single neighbor to contact, and the lack of global information makes it difficult to make any sort of principled choice. As such, researchers have focused on the uniform gossip algorithm, in which each node independently selects a neighbor uniformly at random. When the graph is well-connected, this works quite well. In a string of beautiful papers, researchers proved a sequence of successively stronger bounds on the number of rounds required in terms of the conductance $\phi$ and graph size $n$, culminating in a bound of $O(\phi^{-1} \log n)$. In this paper, we show that a fairly simple modification of the protocol gives an algorithm that solves the information dissemination problem in at most $O(D + \polylog(n))$ rounds in a network of diameter $D$, with no dependence on the conductance. This is at most an additive polylogarithmic factor from the trivial lower bound of $D$, which applies even in the LOCAL model. In fact, we prove that something stronger is true: any algorithm that requires $T$ rounds in the LOCAL model can be simulated in $O(T + \polylog(n))$ rounds in the GOSSIP model. We thus prove that these two models of distributed computation are essentially equivalent.", acknowledgement = ack-nhfb, } @InProceedings{Bansal:2012:TTS, author = "Nikhil Bansal and Vibhor Bhatt and Prasad Jayanti and Ranganath Kondapally", title = "Tight time-space tradeoff for mutual exclusion", crossref = "ACM:2012:SPA", pages = "971--982", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214065", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Mutual Exclusion is a fundamental problem in distributed computing, and the problem of proving upper and lower bounds on the RMR complexity of this problem has been extensively studied. Here, we give matching lower and upper bounds on how RMR complexity trades off with space. Two implications of our results are that constant RMR complexity is impossible with subpolynomial space and subpolynomial RMR complexity is impossible with constant space for cache-coherent multiprocessors, regardless of how strong the hardware synchronization operations are. To prove these results we show that the complexity of mutual exclusion, which can be ``messy'' to analyze because of system details such as asynchrony and cache coherence, is captured precisely by a simple and purely combinatorial game that we design. We then derive lower and upper bounds for this game, thereby obtaining corresponding bounds for mutual exclusion. The lower bounds for the game are proved using potential functions.", acknowledgement = ack-nhfb, } @InProceedings{Giakkoupis:2012:TRL, author = "George Giakkoupis and Philipp Woelfel", title = "A tight {RMR} lower bound for randomized mutual exclusion", crossref = "ACM:2012:SPA", pages = "983--1002", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214066", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "The Cache Coherent (CC) and the Distributed Shared Memory (DSM) models are standard shared memory models, and the Remote Memory Reference (RMR) complexity is considered to accurately predict the actual performance of mutual exclusion algorithms in shared memory systems. In this paper we prove a tight lower bound for the RMR complexity of deadlock-free randomized mutual exclusion algorithms in both the CC and the DSM model with atomic registers and compare \& swap objects and an adaptive adversary. Our lower bound establishes that an adaptive adversary can schedule $n$ processes in such a way that each enters the critical section once, and the total number of RMRs is $\Omega(n \log n/\log \log n)$ in expectation. This matches an upper bound of Hendler and Woelfel (2011).", acknowledgement = ack-nhfb, } @InProceedings{Garg:2012:CPA, author = "Jugal Garg and Ruta Mehta and Milind Sohoni and Vijay V. Vazirani", title = "A complementary pivot algorithm for markets under separable, piecewise-linear concave utilities", crossref = "ACM:2012:SPA", pages = "1003--1016", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214068", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Using the powerful machinery of the linear complementarity problem and Lemke's algorithm, we give a practical algorithm for computing an equilibrium for Arrow--Debreu markets under separable, piecewise-linear concave (SPLC) utilities, despite the PPAD-completeness of this case. As a corollary, we obtain the first elementary proof of existence of equilibrium for this case, i.e., without using fixed point theorems. In 1975, Eaves [10] had given such an algorithm for the case of linear utilities and had asked for an extension to the piecewise-linear, concave utilities. Our result settles the relevant subcase of his problem as well as the problem of Vazirani and Yannakakis of obtaining a path following algorithm for SPLC markets, thereby giving a direct proof of membership of this case in PPAD. We also prove that SPLC markets have an odd number of equilibria (up to scaling), hence matching the classical result of Shapley about 2-Nash equilibria [24], which was based on the Lemke--Howson algorithm. For the linear case, Eaves had asked for a combinatorial interpretation of his algorithm. We provide this and it yields a particularly simple proof of the fact that the set of equilibrium prices is convex.", acknowledgement = ack-nhfb, } @InProceedings{Azar:2012:RP, author = "Pablo Daniel Azar and Silvio Micali", title = "Rational proofs", crossref = "ACM:2012:SPA", pages = "1017--1028", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214069", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We study a new type of proof system, where an unbounded prover and a polynomial time verifier interact, on inputs a string $x$ and a function $f$, so that the Verifier may learn $f(x)$. The novelty of our setting is that there no longer are ``good'' or ``malicious'' provers, but only rational ones. In essence, the Verifier has a budget $c$ and gives the Prover a reward $r \in [0,c]$ determined by the transcript of their interaction; the prover wishes to maximize his expected reward; and his reward is maximized only if he the verifier correctly learns $f(x)$. Rational proof systems are as powerful as their classical counterparts for polynomially many rounds of interaction, but are much more powerful when we only allow a constant number of rounds. Indeed, we prove that if $f \in \#P$, then $f$ is computable by a one-round rational Merlin--Arthur game, where, on input $x$, Merlin's single message actually consists of sending just the value $f(x)$. Further, we prove that CH, the counting hierarchy, coincides with the class of languages computable by a constant-round rational Merlin--Arthur game. Our results rely on a basic and crucial connection between rational proof systems and proper scoring rules, a tool developed to elicit truthful information from experts.", acknowledgement = ack-nhfb, } @InProceedings{Abernethy:2012:MOP, author = "Jacob Abernethy and Rafael M. Frongillo and Andre Wibisono", title = "Minimax option pricing meets {Black--Scholes} in the limit", crossref = "ACM:2012:SPA", pages = "1029--1040", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214070", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Option contracts are a type of financial derivative that allow investors to hedge risk and speculate on the variation of an asset's future market price. In short, an option has a particular payout that is based on the market price for an asset on a given date in the future. In 1973, Black and Scholes proposed a valuation model for options that essentially estimates the tail risk of the asset price under the assumption that the price will fluctuate according to geometric Brownian motion. A key element of their analysis is that the investor can ``hedge'' the payout of the option by continuously buying and selling the asset depending on the price fluctuations. More recently, DeMarzo et al. proposed a more robust valuation scheme which does not require any assumption on the price path; indeed, in their model the asset's price can even be chosen adversarially. This framework can be considered as a sequential two-player zero-sum game between the investor and Nature. We analyze the value of this game in the limit, where the investor can trade at smaller and smaller time intervals. Under weak assumptions on the actions of Nature (an adversary), we show that the minimax option price asymptotically approaches exactly the Black--Scholes valuation. The key piece of our analysis is showing that Nature's minimax optimal dual strategy converges to geometric Brownian motion in the limit.", acknowledgement = ack-nhfb, } @InProceedings{Mossel:2012:QGS, author = "Elchanan Mossel and Mikl{\'o}s Z. R{\'a}cz", title = "A quantitative {Gibbard--Satterthwaite} theorem without neutrality", crossref = "ACM:2012:SPA", pages = "1041--1060", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214071", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Recently, quantitative versions of the Gibbard--Satterthwaite theorem were proven for $k = 3$ alternatives by Friedgut, Kalai, Keller and Nisan and for neutral functions on $k \geq 4$ alternatives by Isaksson, Kindler and Mossel. In the present paper we prove a quantitative version of the Gibbard--Satterthwaite theorem for general social choice functions for any number $k \geq 3$ of alternatives. In particular we show that for a social choice function $f$ on $k \geq 3$ alternatives and $n$ voters, which is $\epsilon$-far from the family of nonmanipulable functions, a uniformly chosen voter profile is manipulable with probability at least inverse polynomial in $n$, $k$, and $\epsilon^{-1}$. Removing the neutrality assumption of previous theorems is important for multiple reasons. For one, it is known that there is a conflict between anonymity and neutrality, and since most common voting rules are anonymous, they cannot always be neutral. Second, virtual elections are used in many applications in artificial intelligence, where there are often restrictions on the outcome of the election, and so neutrality is not a natural assumption in these situations. Ours is a unified proof which in particular covers all previous cases established before. The proof crucially uses reverse hypercontractivity in addition to several ideas from the two previous proofs. Much of the work is devoted to understanding functions of a single voter, and in particular we also prove a quantitative Gibbard--Satterthwaite theorem for one voter.", acknowledgement = ack-nhfb, } @InProceedings{Bourgain:2012:ME, author = "Jean Bourgain and Amir Yehudayoff", title = "Monotone expansion", crossref = "ACM:2012:SPA", pages = "1061--1078", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214073", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "This work presents an explicit construction of a family of monotone expanders, which are bi-partite expander graphs whose edge-set is defined by (partial) monotone functions. The family is essentially defined by the M{\"o}bius action of ${\rm SL}_2(R)$, the group of $2 \times 2$ matrices with determinant one, on the interval $[0, 1]$. No other proof-of-existence for monotone expanders is known, not even using the probabilistic method. The proof extends recent results on finite/compact groups to the non-compact scenario. Specifically, we show a product-growth theorem for ${\rm SL}_2(R)$; roughly, that for every $A \subset {\rm SL}_2(R)$ with certain properties, the size of $AAA$ is much larger than that of $A$. We mention two applications of this construction: Dvir and Shpilka showed that it yields a construction of explicit dimension expanders, which are a generalization of standard expander graphs. Dvir and Wigderson proved that it yields the existence of explicit pushdown expanders, which are graphs that arise in Turing machine simulations.", acknowledgement = ack-nhfb, } @InProceedings{Alon:2012:NCG, author = "Noga Alon and Ankur Moitra and Benny Sudakov", title = "Nearly complete graphs decomposable into large induced matchings and their applications", crossref = "ACM:2012:SPA", pages = "1079--1090", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214074", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We describe two constructions of (very) dense graphs which are edge disjoint unions of large {\em induced\/} matchings. The first construction exhibits graphs on $N$ vertices with ${N \choose 2} - o(N^2)$ edges, which can be decomposed into pairwise disjoint induced matchings, each of size $N^{1 - o(1)}$. The second construction provides a covering of all edges of the complete graph $K_N$ by two graphs, each being the edge disjoint union of at most $N^{2 - \delta}$ induced matchings, where $\delta > 0.076$. This disproves (in a strong form) a conjecture of Meshulam, substantially improves a result of Birk, Linial and Meshulam on communicating over a shared channel, and (slightly) extends the analysis of Hastad and Wigderson of the graph test of Samorodnitsky and Trevisan for linearity. Additionally, our constructions settle a combinatorial question of Vempala regarding a candidate rounding scheme for the directed Steiner tree problem.", acknowledgement = ack-nhfb, } @InProceedings{Kuperberg:2012:PER, author = "Greg Kuperberg and Shachar Lovett and Ron Peled", title = "Probabilistic existence of rigid combinatorial structures", crossref = "ACM:2012:SPA", pages = "1091--1106", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214075", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We show the existence of rigid combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, $t$-designs, and $t$-wise permutations. In all cases, the sizes of the objects are optimal up to polynomial overhead. The proof of existence is probabilistic. We show that a randomly chosen such object has the required properties with positive yet tiny probability. The main technical ingredient is a special local central limit theorem for suitable lattice random walks with finitely many steps.", acknowledgement = ack-nhfb, } @InProceedings{Dobzinski:2012:QCC, author = "Shahar Dobzinski and Jan Vondrak", title = "From query complexity to computational complexity", crossref = "ACM:2012:SPA", pages = "1107--1116", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214076", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We consider submodular optimization problems, and provide a general way of translating oracle inapproximability results arising from the symmetry gap technique to computational complexity inapproximability results, where the submodular function is given explicitly (under the assumption that NP $\not=$ RP). Applications of our technique include an optimal computational hardness of $(1/2 + \epsilon)$-approximation for maximizing a symmetric nonnegative submodular function, an optimal hardness of $(1 - (1 - 1 / k)^k + \epsilon)$-approximation for welfare maximization in combinatorial auctions with $k$ submodular bidders (for constant $k$), super-constant hardness for maximizing a nonnegative submodular function over matroid bases, and tighter bounds for maximizing a monotone submodular function subject to a cardinality constraint. Unlike the vast majority of computational inapproximability results, our approach does not use the PCP machinery or the Unique Games Conjecture, but relies instead on a direct reduction from Unique-SAT using list-decodable codes.", acknowledgement = ack-nhfb, } @InProceedings{Lee:2012:MWS, author = "James R. Lee and Shayan Oveis Gharan and Luca Trevisan", title = "Multi-way spectral partitioning and higher-order {Cheeger} inequalities", crossref = "ACM:2012:SPA", pages = "1117--1130", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214078", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "A basic fact in spectral graph theory is that the number of connected components in an undirected graph is equal to the multiplicity of the eigenvalue zero in the Laplacian matrix of the graph. In particular, the graph is disconnected if and only if there are at least two eigenvalues equal to zero. Cheeger's inequality and its variants provide an approximate version of the latter fact; they state that a graph has a sparse cut if and only if there are at least two eigenvalues that are close to zero. It has been conjectured that an analogous characterization holds for higher multiplicities, i.e., there are $k$ eigenvalues close to zero if and only if the vertex set can be partitioned into $k$ subsets, each defining a sparse cut. We resolve this conjecture. Our result provides a theoretical justification for clustering algorithms that use the bottom $k$ eigenvectors to embed the vertices into R$^k$, and then apply geometric considerations to the embedding. We also show that these techniques yield a nearly optimal quantitative connection between the expansion of sets of size $\approx n/k$ and $\lambda_k$, the $k$th smallest eigenvalue of the normalized Laplacian, where $n$ is the number of vertices. In particular, we show that in every graph there are at least $k / 2$ disjoint sets (one of which will have size at most $2 n / k$), each having expansion at most $O(\sqrt{\lambda_k \log k})$. Louis, Raghavendra, Tetali, and Vempala have independently proved a slightly weaker version of this last result [LRTV12]. The $\sqrt{\log k}$ bound is tight, up to constant factors, for the ``noisy hypercube'' graphs.", acknowledgement = ack-nhfb, } @InProceedings{Louis:2012:MSC, author = "Anand Louis and Prasad Raghavendra and Prasad Tetali and Santosh Vempala", title = "Many sparse cuts via higher eigenvalues", crossref = "ACM:2012:SPA", pages = "1131--1140", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214079", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Cheeger's fundamental inequality states that any edge-weighted graph has a vertex subset $S$ such that its expansion (a.k.a. conductance) is bounded as follows:\par $$\phi(S) {\hbox{\tiny \rm def} \atop =} (w(S, \bar{S})) / \min \{w(S), w(\bar{S})\} \leq \sqrt{2 \lambda_2}$$\par where $w$ is the total edge weight of a subset or a cut and $\lambda_2$ is the second smallest eigenvalue of the normalized Laplacian of the graph. Here we prove the following natural generalization: for any integer $k \in [n]$, there exist $c k$ disjoint subsets $S_1$, \ldots{}, $S_{c k}$, such that\par $$\max_i \phi(S_i) \leq C \sqrt{\lambda_k \log k}$$\par where $\lambda_k$ is the $k$th smallest eigenvalue of the normalized Laplacian and $c < 1$, $C > 0$ are suitable absolute constants. Our proof is via a polynomial-time algorithm to find such subsets, consisting of a spectral projection and a randomized rounding. As a consequence, we get the same upper bound for the small set expansion problem, namely for any $k$, there is a subset $S$ whose weight is at most a $O(1/k)$ fraction of the total weight and $\phi(S) \leq C \sqrt{\lambda_k \log k}$. Both results are the best possible up to constant factors.\par The underlying algorithmic problem, namely finding $k$ subsets such that the maximum expansion is minimized, besides extending sparse cuts to more than one subset, appears to be a natural clustering problem in its own right.", acknowledgement = ack-nhfb, } @InProceedings{Orecchia:2012:AEL, author = "Lorenzo Orecchia and Sushant Sachdeva and Nisheeth K. Vishnoi", title = "Approximating the exponential, the {Lanczos} method and an {$\tilde{O}(m)$}-time spectral algorithm for balanced separator", crossref = "ACM:2012:SPA", pages = "1141--1160", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214080", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We give a novel spectral approximation algorithm for the balanced (edge-)separator problem that, given a graph $G$, a constant balance $b \in (0,1/2]$, and a parameter $\gamma$, either finds an $\Omega(b)$-balanced cut of conductance $O(\sqrt \gamma)$ in $G$, or outputs a certificate that all $b$-balanced cuts in $G$ have conductance at least $\gamma$, and runs in time $\tilde{O}(m)$. This settles the question of designing asymptotically optimal spectral algorithms for balanced separator. Our algorithm relies on a variant of the heat kernel random walk and requires, as a subroutine, an algorithm to compute $\exp(-L) v$ where $L$ is the Laplacian of a graph related to $G$ and $v$ is a vector. Algorithms for computing the matrix-exponential-vector product efficiently comprise our next set of results. Our main result here is a new algorithm which computes a good approximation to $\exp(-A) v$ for a class of symmetric positive semidefinite (PSD) matrices $A$ and a given vector $v$, in time roughly $\tilde{O}(m_A)$, independent of the norm of $A$, where $m_A$ is the number of non-zero entries of $A$. This uses, in a non-trivial way, the result of Spielman and Teng on inverting symmetric and diagonally-dominant matrices in $\tilde{O}(m_A)$ time. Finally, using old and new uniform approximations to $e^{-x}$ we show how to obtain, via the Lanczos method, a simple algorithm to compute $\exp(-A) v$ for symmetric PSD matrices that runs in time roughly $O(t_A \cdot \sqrt{\norm(A)})$, where $t_A$ is the time required for the computation of the vector $A w$ for given vector w. As an application, we obtain a simple and practical algorithm, with output conductance $O(\sqrt \gamma)$, for balanced separator that runs in time $O(m / \sqrt \gamma)$. This latter algorithm matches the running time, but improves on the approximation guarantee of the Evolving-Sets-based algorithm by Andersen and Peres for balanced separator.", acknowledgement = ack-nhfb, } @InProceedings{Goemans:2012:MIG, author = "Michel X. Goemans and Neil Olver and Thomas Rothvo{\ss} and Rico Zenklusen", title = "Matroids and integrality gaps for hypergraphic {Steiner} tree relaxations", crossref = "ACM:2012:SPA", pages = "1161--1176", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214081", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Until recently, LP relaxations have only played a very limited role in the design of approximation algorithms for the Steiner tree problem. In particular, no (efficiently solvable) Steiner tree relaxation was known to have an integrality gap bounded away from $2$, before Byrka et al. [3] showed an upper bound of $\approx 1.55$ of a hypergraphic LP relaxation and presented a $\ln(4) + \epsilon \approx 1.39$ approximation based on this relaxation. Interestingly, even though their approach is LP based, they do not compare the solution produced against the LP value.\par We take a fresh look at hypergraphic LP relaxations for the Steiner tree problem --- one that heavily exploits methods and results from the theory of matroids and submodular functions --- which leads to stronger integrality gaps, faster algorithms, and a variety of structural insights of independent interest. More precisely, along the lines of the algorithm of Byrka et al.[3], we present a deterministic $\ln(4) + \epsilon$ approximation that compares against the LP value and therefore proves a matching $\ln(4)$ upper bound on the integrality gap of hypergraphic relaxations.\par Similarly to [3], we iteratively fix one component and update the LP solution. However, whereas in [3] the LP is solved at every iteration after contracting a component, we show how feasibility can be maintained by a greedy procedure on a well-chosen matroid. Apart from avoiding the expensive step of solving a hypergraphic LP at each iteration, our algorithm can be analyzed using a simple potential function. This potential function gives an easy means to determine stronger approximation guarantees and integrality gaps when considering restricted graph topologies. In particular, this readily leads to a $73/60 \approx 1.217$ upper bound on the integrality gap of hypergraphic relaxations for quasi-bipartite graphs.\par Additionally, for the case of quasi-bipartite graphs, we present a simple algorithm to transform an optimal solution to the bidirected cut relaxation to an optimal solution of the hypergraphic relaxation, leading to a fast $73/60$ approximation for quasi-bipartite graphs. Furthermore, we show how the separation problem of the hypergraphic relaxation can be solved by computing maximum flows, which provides a way to obtain a fast independence oracle for the matroids that we use in our approach.", acknowledgement = ack-nhfb, } @InProceedings{Brodal:2012:SFH, author = "Gerth St{\o}lting Brodal and George Lagogiannis and Robert E. Tarjan", title = "Strict {Fibonacci} heaps", crossref = "ACM:2012:SPA", pages = "1177--1184", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214082", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We present the first pointer-based heap implementation with time bounds matching those of Fibonacci heaps in the worst case. We support make-heap, insert, find-min, meld and decrease-key in worst-case $O(1)$ time, and delete and delete-min in worst-case $O(\lg n)$ time, where $n$ is the size of the heap. The data structure uses linear space. A previous, very complicated, solution achieving the same time bounds in the RAM model made essential use of arrays and extensive use of redundant counter schemes to maintain balance. Our solution uses neither. Our key simplification is to discard the structure of the smaller heap when doing a meld. We use the pigeonhole principle in place of the redundant counter mechanism.", acknowledgement = ack-nhfb, } @InProceedings{Bulnek:2012:TLB, author = "Jan Bul{\'a}nek and Michal Kouck{\'y} and Michael Saks", title = "Tight lower bounds for the online labeling problem", crossref = "ACM:2012:SPA", pages = "1185--1198", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214083", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We consider the file maintenance problem (also called the online labeling problem) in which $n$ integer items from the set $\{1, \ldots{}, r\}$ are to be stored in an array of size $m \geq n$. The items are presented sequentially in an arbitrary order, and must be stored in the array in sorted order (but not necessarily in consecutive locations in the array). Each new item must be stored in the array before the next item is received. If $r \leq m$ then we can simply store item $j$ in location $j$ but if $r > m$ then we may have to shift the location of stored items to make space for a newly arrived item. The algorithm is charged each time an item is stored in the array, or moved to a new location. The goal is to minimize the total number of such moves the algorithm has to do. This problem is non-trivial when $n \leq m < r$. In the case that $m = Cn$ for some $C > 1$, algorithms for this problem with cost $O(\log(n)^2)$ per item have been given [Itai et al. (1981), Willard (1992), Bender et al. (2002)]. When $m = n$, algorithms with cost $O(\log(n)^3)$ per item were given [Zhang (1993),Bird and Sadnicki (2007)]. In this paper we prove lower bounds that show that these algorithms are optimal, up to constant factors. Previously, the only lower bound known for this range of parameters was a lower bound of $\Omega(\log(n)^2)$ for the restricted class of smooth algorithms [Dietz et al. (2005), Zhang (1993)]. We also provide an algorithm for the sparse case: If the number of items is polylogarithmic in the array size then the problem can be solved in amortized constant time per item.", acknowledgement = ack-nhfb, } @InProceedings{Abraham:2012:FDA, author = "Ittai Abraham and Shiri Chechik and Cyril Gavoille", title = "Fully dynamic approximate distance oracles for planar graphs via forbidden-set distance labels", crossref = "ACM:2012:SPA", pages = "1199--1218", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214084", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "This paper considers fully dynamic $(1 + \epsilon)$ distance oracles and $(1 + \epsilon)$ forbidden-set labeling schemes for planar graphs. For a given $n$-vertex planar graph $G$ with edge weights drawn from $[1,M]$ and parameter $\epsilon > 0$, our forbidden-set labeling scheme uses labels of length $\lambda = O(\epsilon^{-1} \log^2 n \log (n M) \cdot \log n)$. Given the labels of two vertices $s$ and $t$ and of a set $F$ of faulty vertices\slash edges, our scheme approximates the distance between $s$ and $t$ in $G \backslash F$ with stretch $(1 + \epsilon)$, in $O(|F|^2 \lambda)$ time.\par We then present a general method to transform $(1 + \epsilon)$ forbidden-set labeling schemas into a fully dynamic $(1 + \epsilon)$ distance oracle. Our fully dynamic $(1 + \epsilon)$ distance oracle is of size $O(n \log n \cdot (\epsilon^{-1} + \log n))$ and has $\tilde{O}(n^{1/2})$ query and update time, both the query and the update time are worst case. This improves on the best previously known $(1 + \epsilon)$ dynamic distance oracle for planar graphs, which has worst case query time $\tilde{O}(n^{2/3})$ and amortized update time of $\tilde{O}(n^{2/3})$.\par Our $(1 + \epsilon)$ forbidden-set labeling scheme can also be extended into a forbidden-set labeled routing scheme with stretch $(1 + \epsilon)$.", acknowledgement = ack-nhfb, } @InProceedings{Lopez-Alt:2012:FMC, author = "Adriana L{\'o}pez-Alt and Eran Tromer and Vinod Vaikuntanathan", title = "On-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption", crossref = "ACM:2012:SPA", pages = "1219--1234", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214086", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We propose a new notion of secure multiparty computation aided by a computationally-powerful but untrusted ``cloud'' server. In this notion that we call on-the-fly multiparty computation (MPC), the cloud can non-interactively perform arbitrary, dynamically chosen computations on data belonging to arbitrary sets of users chosen on-the-fly. All user's input data and intermediate results are protected from snooping by the cloud as well as other users. This extends the standard notion of fully homomorphic encryption (FHE), where users can only enlist the cloud's help in evaluating functions on their own encrypted data. In on-the-fly MPC, each user is involved only when initially uploading his (encrypted) data to the cloud, and in a final output decryption phase when outputs are revealed; the complexity of both is independent of the function being computed and the total number of users in the system. When users upload their data, they need not decide in advance which function will be computed, nor who they will compute with; they need only retroactively approve the eventually-chosen functions and on whose data the functions were evaluated. This notion is qualitatively the best possible in minimizing interaction, since the users' interaction in the decryption stage is inevitable: we show that removing it would imply generic program obfuscation and is thus impossible. Our contributions are two-fold:- We show how on-the-fly MPC can be achieved using a new type of encryption scheme that we call multikey FHE, which is capable of operating on inputs encrypted under multiple, unrelated keys. A ciphertext resulting from a multikey evaluation can be jointly decrypted using the secret keys of all the users involved in the computation. --- We construct a multikey FHE scheme based on NTRU, a very efficient public-key encryption scheme proposed in the 1990s. It was previously not known how to make NTRU fully homomorphic even for a single party. We view the construction of (multikey) FHE from NTRU encryption as a main contribution of independent interest. Although the transformation to a fully homomorphic system deteriorates the efficiency of NTRU somewhat, we believe that this system is a leading candidate for a practical FHE scheme.", acknowledgement = ack-nhfb, } @InProceedings{Boyle:2012:MCS, author = "Elette Boyle and Shafi Goldwasser and Abhishek Jain and Yael Tauman Kalai", title = "Multiparty computation secure against continual memory leakage", crossref = "ACM:2012:SPA", pages = "1235--1254", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214087", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We construct a multiparty computation (MPC) protocol that is secure even if a malicious adversary, in addition to corrupting $1 - \epsilon$ fraction of all parties for an arbitrarily small constant $\epsilon > 0$, can leak information about the secret state of each honest party. This leakage can be continuous for an unbounded number of executions of the MPC protocol, computing different functions on the same or different set of inputs. We assume a (necessary) ``leak-free'' preprocessing stage. We emphasize that we achieve leakage resilience without weakening the security guarantee of classical MPC. Namely, an adversary who is given leakage on honest parties' states, is guaranteed to learn nothing beyond the input and output values of corrupted parties. This is in contrast with previous works on leakage in the multi-party protocol setting, which weaken the security notion, and only guarantee that a protocol which leaks $l$ bits about the parties' secret states, yields at most $l$ bits of leakage on the parties' private inputs. For some functions, such as voting, such leakage can be detrimental. Our result relies on standard cryptographic assumptions, and our security parameter is polynomially related to the number of parties.", acknowledgement = ack-nhfb, } @InProceedings{Hardt:2012:BRR, author = "Moritz Hardt and Aaron Roth", title = "Beating randomized response on incoherent matrices", crossref = "ACM:2012:SPA", pages = "1255--1268", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214088", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Computing accurate low rank approximations of large matrices is a fundamental data mining task. In many applications however the matrix contains sensitive information about individuals. In such case we would like to release a low rank approximation that satisfies a strong privacy guarantee such as differential privacy. Unfortunately, to date the best known algorithm for this task that satisfies differential privacy is based on naive input perturbation or randomized response: Each entry of the matrix is perturbed independently by a sufficiently large random noise variable, a low rank approximation is then computed on the resulting matrix. We give (the first) significant improvements in accuracy over randomized response under the natural and necessary assumption that the matrix has low coherence. Our algorithm is also very efficient and finds a constant rank approximation of an $m \times n$ matrix in time $O(m n)$. Note that even generating the noise matrix required for randomized response already requires time $O(mn)$.", acknowledgement = ack-nhfb, } @InProceedings{Bhaskara:2012:UDP, author = "Aditya Bhaskara and Daniel Dadush and Ravishankar Krishnaswamy and Kunal Talwar", title = "Unconditional differentially private mechanisms for linear queries", crossref = "ACM:2012:SPA", pages = "1269--1284", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214089", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We investigate the problem of designing differentially private mechanisms for a set of $d$ linear queries over a database, while adding as little error as possible. Hardt and Talwar [HT10] related this problem to geometric properties of a convex body defined by the set of queries and gave a $O(\log^3 d)$-approximation to the minimum $l_2^2$ error, assuming a conjecture from convex geometry called the Slicing or Hyperplane conjecture. In this work we give a mechanism that works unconditionally, and also gives an improved $O(\log^2 d)$ approximation to the expected $l_2^2$ error. We remove the dependence on the Slicing conjecture by using a result of Klartag [Kla06] that shows that any convex body is close to one for which the conjecture holds; our main contribution is in making this result constructive by using recent techniques of Dadush, Peikert and Vempala [DPV10]. The improvement in approximation ratio relies on a stronger lower bound we derive on the optimum. This new lower bound goes beyond the packing argument that has traditionally been used in Differential Privacy and allows us to add the packing lower bounds obtained from orthogonal subspaces. We are able to achieve this via a symmetrization argument which argues that there always exists a near optimal differentially private mechanism which adds noise that is independent of the input database! We believe this result should be of independent interest, and also discuss some interesting consequences.", acknowledgement = ack-nhfb, } @InProceedings{Muthukrishnan:2012:OPH, author = "S. Muthukrishnan and Aleksandar Nikolov", title = "Optimal private halfspace counting via discrepancy", crossref = "ACM:2012:SPA", pages = "1285--1292", year = "2012", DOI = "https://doi.org/10.1145/2213977.2214090", bibdate = "Thu Nov 8 19:11:58 MST 2012", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "A {\em range counting\/} problem is specified by a set $P$ of size $|P| = n$ of points in $\mathbb{R}^d$, an integer {\em weight\/} $x_p$ associated to each point $p \in P$, and a {\em range space\/} ${\cal R} \subseteq 2^P$. Given a query range $R \in {\cal R}$, the output is $R(x) = \sum_{p \in R} x_p$. The {\em average squared error\/} of an algorithm ${\cal A}$ is $1/|R| \sum_{R \in {\cal R}} ({\cal A}(R, x) - R(x))^2$. Range counting for different range spaces is a central problem in Computational Geometry.\par We study $(\epsilon, \delta)$-differentially private algorithms for range counting. Our main results are for the range space given by hyperplanes, that is, the halfspace counting problem. We present an $(\epsilon, \delta)$-differentially private algorithm for halfspace counting in $d$ dimensions which is $O(n^{1 - 1/d})$ approximate for average squared error. This contrasts with the $\Omega(n)$ lower bound established by the classical result of Dinur and Nissim on approximation for arbitrary subset counting queries. We also show a matching lower bound of $\Omega(n^{1 - 1 /d})$ approximation for any $(\epsilon, \delta)$-differentially private algorithm for halfspace counting.\par Both bounds are obtained using discrepancy theory. For the lower bound, we use a modified discrepancy measure and bound approximation of $(\epsilon, \delta)$-differentially private algorithms for range counting queries in terms of this discrepancy. We also relate the modified discrepancy measure to classical combinatorial discrepancy, which allows us to exploit known discrepancy lower bounds. This approach also yields a lower bound of $\Omega((\log n)^{d - 1})$ for $(\epsilon, \delta)$-differentially private {\em orthogonal\/} range counting in $d$ dimensions, the first known superconstant lower bound for this problem. For the upper bound, we use an approach inspired by partial coloring methods for proving discrepancy upper bounds, and obtain $(\epsilon, \delta)$-differentially private algorithms for range counting with polynomially bounded shatter function range spaces.", acknowledgement = ack-nhfb, } @InProceedings{Kane:2013:PLF, author = "Daniel M. Kane and Raghu Meka", title = "A {PRG} for {Lipschitz} functions of polynomials with applications to sparsest cut", crossref = "ACM:2013:SPF", pages = "1--10", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488610", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/prng.bib; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We give improved pseudorandom generators (PRGs) for Lipschitz functions of low-degree polynomials over the hypercube. These are functions of the form $ \psi (P(x)) $, where $ P : {1, - 1}^n \to R $ is a low-degree polynomial and $ \psi : R \to R $ is a function with small Lipschitz constant. PRGs for smooth functions of low-degree polynomials have received a lot of attention recently and play an important role in constructing PRGs for the natural class of polynomial threshold functions [12,13,24,16,15]. In spite of the recent progress, no nontrivial PRGs were known for fooling Lipschitz functions of degree $ O(\log n) $ polynomials even for constant error rate. In this work, we give the first such generator obtaining a seed-length of $ (\log n) O(l^2 / \epsilon^2) $ for fooling degree $l$ polynomials with error $ \epsilon $. Previous generators had an exponential dependence on the degree $l$. We use our PRG to get better integrality gap instances for sparsest cut, a fundamental problem in graph theory with many applications in graph optimization. We give an instance of uniform sparsest cut for which a powerful semi-definite relaxation (SDP) first introduced by Goemans and Linial and studied in the seminal work of Arora, Rao and Vazirani [3] has an integrality gap of $ \exp (\Omega ((\log \log n)^{1 / 2})) $. Understanding the performance of the Goemans--Linial SDP for uniform sparsest cut is an important open problem in approximation algorithms and metric embeddings. Our work gives a near-exponential improvement over previous lower bounds which achieved a gap of $ \Omega (\log \log n) $ [11,21]. Our gap instance builds on the recent short code gadgets of Barak et al. [5].", acknowledgement = ack-nhfb, } @InProceedings{Kwok:2013:ICI, author = "Tsz Chiu Kwok and Lap Chi Lau and Yin Tat Lee and Shayan Oveis Gharan and Luca Trevisan", title = "Improved {Cheeger}'s inequality: analysis of spectral partitioning algorithms through higher order spectral gap", crossref = "ACM:2013:SPF", pages = "11--20", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488611", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Let $ \phi (G) $ be the minimum conductance of an undirected graph $G$, and let $ 0 = \lambda_1 \leq \lambda_2 \leq \ldots {} \leq \lambda_n \leq 2 $ be the eigenvalues of the normalized Laplacian matrix of $G$. We prove that for any graph $G$ and any $ k \geq 2 $, $ [\phi (G) = O(k) l_2 / \sqrt l_k] $, and this performance guarantee is achieved by the spectral partitioning algorithm. This improves Cheeger's inequality, and the bound is optimal up to a constant factor for any $k$. Our result shows that the spectral partitioning algorithm is a constant factor approximation algorithm for finding a sparse cut if $ l_k $ is a constant for some constant $k$. This provides some theoretical justification to its empirical performance in image segmentation and clustering problems. We extend the analysis to spectral algorithms for other graph partitioning problems, including multi-way partition, balanced separator, and maximum cut.", acknowledgement = ack-nhfb, } @InProceedings{Williams:2013:NPV, author = "Ryan Williams", title = "Natural proofs versus derandomization", crossref = "ACM:2013:SPF", pages = "21--30", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488612", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We study connections between Natural Proofs, derandomization, and the problem of proving ``weak'' circuit lower bounds such as $ {\rm NEXP} \not \subset {\rm TC}^0 $, which are still wide open. Natural Proofs have three properties: they are constructive (an efficient algorithm $A$ is embedded in them), have largeness ($A$ accepts a large fraction of strings), and are useful ($A$ rejects all strings which are truth tables of small circuits). Strong circuit lower bounds that are ``naturalizing'' would contradict present cryptographic understanding, yet the vast majority of known circuit lower bound proofs are naturalizing. So it is imperative to understand how to pursue un-Natural Proofs. Some heuristic arguments say constructivity should be circumventable. Largeness is inherent in many proof techniques, and it is probably our presently weak techniques that yield constructivity. We prove: Constructivity is unavoidable, even for NEXP lower bounds. Informally, we prove for all ``typical'' non-uniform circuit classes $C$, $ {\rm NEXP} \not \subset C $ if and only if there is a polynomial-time algorithm distinguishing some function from all functions computable by $C$-circuits. Hence $ {\rm NEXP} \not \subset C $ is equivalent to exhibiting a constructive property useful against $C$. There are no P-natural properties useful against $C$ if and only if randomized exponential time can be ``derandomized'' using truth tables of circuits from $C$ as random seeds. Therefore the task of proving there are no $P$-natural properties is inherently a derandomization problem, weaker than but implied by the existence of strong pseudorandom functions. These characterizations are applied to yield several new results. The two main applications are that $ {\rm NEXP} \cap {\rm coNEXP} $ does not have $ n^{\log n} $ size ACC circuits, and a mild derandomization result for RP.", acknowledgement = ack-nhfb, } @InProceedings{Bei:2013:CTE, author = "Xiaohui Bei and Ning Chen and Shengyu Zhang", title = "On the complexity of trial and error", crossref = "ACM:2013:SPF", pages = "31--40", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488613", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Motivated by certain applications from physics, biochemistry, economics, and computer science in which the objects under investigation are unknown or not directly accessible because of various limitations, we propose a trial-and-error model to examine search problems in which inputs are unknown. More specifically, we consider constraint satisfaction problems $ \wedge_i C_i $, where the constraints $ C_i $ are hidden, and the goal is to find a solution satisfying all constraints. We can adaptively propose a candidate solution (i.e., trial), and there is a verification oracle that either confirms that it is a valid solution, or returns the index i of a violated constraint (i.e., error), with the exact content of $ C_i $ still hidden. We studied the time and trial complexities of a number of natural CSPs, summarized as follows. On one hand, despite the seemingly very little information provided by the oracle, efficient algorithms do exist for Nash, Core, Stable Matching, and SAT problems, whose unknown-input versions are shown to be as hard as the corresponding known-input versions up to a factor of polynomial. The techniques employed vary considerably, including, e.g., order theory and the ellipsoid method with a strong separation oracle. On the other hand, there are problems whose complexities are substantially increased in the unknown-input model. In particular, no time-efficient algorithms exist for Graph Isomorphism and Group Isomorphism (unless PH collapses or P = NP). The proofs use quite nonstandard reductions, in which an efficient simulator is carefully designed to simulate a desirable but computationally unaffordable oracle. Our model investigates the value of input information, and our results demonstrate that the lack of input information can introduce various levels of extra difficulty. The model accommodates a wide range of combinatorial and algebraic structures, and exhibits intimate connections with (and hopefully can also serve as a useful supplement to) certain existing learning and complexity theories.", acknowledgement = ack-nhfb, } @InProceedings{Bhawalkar:2013:COF, author = "Kshipra Bhawalkar and Sreenivas Gollapudi and Kamesh Munagala", title = "Coevolutionary opinion formation games", crossref = "ACM:2013:SPF", pages = "41--50", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488615", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We present game-theoretic models of opinion formation in social networks where opinions themselves co-evolve with friendships. In these models, nodes form their opinions by maximizing agreements with friends weighted by the strength of the relationships, which in turn depend on difference in opinion with the respective friends. We define a social cost of this process by generalizing recent work of Bindel et al., FOCS 2011. We tightly bound the price of anarchy of the resulting dynamics via local smoothness arguments, and characterize it as a function of how much nodes value their own (intrinsic) opinion, as well as how strongly they weigh links to friends with whom they agree more.", acknowledgement = ack-nhfb, } @InProceedings{Chawla:2013:PIM, author = "Shuchi Chawla and Jason D. Hartline and David Malec and Balasubramanian Sivan", title = "Prior-independent mechanisms for scheduling", crossref = "ACM:2013:SPF", pages = "51--60", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488616", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We study the makespan minimization problem with unrelated selfish machines under the assumption that job sizes are stochastic. We design simple truthful mechanisms that under different distributional assumptions provide constant and sublogarithmic approximations to expected makespan. Our mechanisms are prior-independent in that they do not rely on knowledge of the job size distributions. Prior-independent approximations were previously known only for the revenue maximization objective [13, 11, 26]. In contrast to our results, in prior-free settings no truthful anonymous deterministic mechanism for the makespan objective can provide a sublinear approximation [3].", acknowledgement = ack-nhfb, } @InProceedings{Feldman:2013:CWE, author = "Michal Feldman and Nick Gravin and Brendan Lucier", title = "Combinatorial {Walrasian Equilibrium}", crossref = "ACM:2013:SPF", pages = "61--70", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488617", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We study a combinatorial market design problem, where a collection of indivisible objects is to be priced and sold to potential buyers subject to equilibrium constraints. The classic solution concept for such problems is Walrasian Equilibrium (WE), which provides a simple and transparent pricing structure that achieves optimal social welfare. The main weakness of the WE notion is that it exists only in very restrictive cases. To overcome this limitation, we introduce the notion of a Combinatorial Walrasian equilibium (CWE), a natural relaxation of WE. The difference between a CWE and a (non-combinatorial) WE is that the seller can package the items into indivisible bundles prior to sale, and the market does not necessarily clear. We show that every valuation profile admits a CWE that obtains at least half of the optimal (unconstrained) social welfare. Moreover, we devise a poly-time algorithm that, given an arbitrary allocation X, computes a CWE that achieves at least half of the welfare of X. Thus, the economic problem of finding a CWE with high social welfare reduces to the algorithmic problem of social-welfare approximation. In addition, we show that every valuation profile admits a CWE that extracts a logarithmic fraction of the optimal welfare as revenue. Finally, these results are complemented by strong lower bounds when the seller is restricted to using item prices only, which motivates the use of bundles. The strength of our results derives partly from their generality --- our results hold for arbitrary valuations that may exhibit complex combinations of substitutes and complements.", acknowledgement = ack-nhfb, } @InProceedings{Naor:2013:ERN, author = "Assaf Naor and Oded Regev and Thomas Vidick", title = "Efficient rounding for the noncommutative {Grothendieck} inequality", crossref = "ACM:2013:SPF", pages = "71--80", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488618", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "The classical Grothendieck inequality has applications to the design of approximation algorithms for NP-hard optimization problems. We show that an algorithmic interpretation may also be given for a noncommutative generalization of the Grothendieck inequality due to Pisier and Haagerup. Our main result, an efficient rounding procedure for this inequality, leads to a constant-factor polynomial time approximation algorithm for an optimization problem which generalizes the Cut Norm problem of Frieze and Kannan, and is shown here to have additional applications to robust principle component analysis and the orthogonal Procrustes problem.", acknowledgement = ack-nhfb, } @InProceedings{Clarkson:2013:LRA, author = "Kenneth L. Clarkson and David P. Woodruff", title = "Low rank approximation and regression in input sparsity time", crossref = "ACM:2013:SPF", pages = "81--90", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488620", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We design a new distribution over $ \poly (r \epsilon^{-1}) \times n $ matrices $S$ so that for any fixed $ n \times d $ matrix $A$ of rank $r$, with probability at least $ 9 / 10 $, $ S A x_2 = (1 \pm \epsilon) A x_2 $ simultaneously for all $ x \in R^d $. Such a matrix $S$ is called a subspace embedding. Furthermore, $ S A $ can be computed in $ O({\rm nnz}(A)) + \tilde O (r^2 \epsilon^{-2}) $ time, where $ {\rm nnz}(A) $ is the number of non-zero entries of $A$. This improves over all previous subspace embeddings, which required at least $ \Omega (n d \log d) $ time to achieve this property. We call our matrices $S$ sparse embedding matrices. Using our sparse embedding matrices, we obtain the fastest known algorithms for overconstrained least-squares regression, low-rank approximation, approximating all leverage scores, and $ l_p $ -regression: to output an $ x' $ for which $ A x' - b_2 \leq (1 + \epsilon) \min_x A x - b_2 $ for an $ n \times d $ matrix $A$ and an $ n \times 1 $ column vector $b$, we obtain an algorithm running in $ O({\rm nnz}(A)) + \tilde O(d^3 \epsilon^{-2}) $ time, and another in $ O({\rm nnz}(A) \log (1 / \epsilon)) + \tilde O(d^3 \log (1 / \epsilon)) $ time. (Here $ \tilde O(f) = f \cdot l o g^{O(1)} (f) $.) to obtain a decomposition of an $ n \times n $ matrix $A$ into a product of an $ n \times k $ matrix $L$, a $ k \times k $ diagonal matrix $D$, and a $ n \times k $ matrix $W$, for which $ \{ F A - L D W \} \leq (1 + \epsilon) F \{ A - A_k \} $, where $ A_k $ is the best rank-$k$ approximation, our algorithm runs in $ O({\rm nnz}(A)) + \tilde O(n k^2 \epsilon^{-4} \log n + k^3 \epsilon^{-5} \log^2 n) $ time. to output an approximation to all leverage scores of an $ n \times d $ input matrix $A$ simultaneously, with constant relative error, our algorithms run in $ O({\rm nnz}(A) \log n) + \tilde O(r^3) $ time. to output an $ x' $ for which $ A x' - b_p \leq (1 + \epsilon) \min_x A x - b_p $ for an $ n \times d $ matrix $A$ and an $ n \times 1 $ column vector $b$, we obtain an algorithm running in $ O({\rm nnz}(A) \log n) + \poly (r \epsilon^{-1}) $ time, for any constant $ 1 \leq p < \infty $. We optimize the polynomial factors in the above stated running times, and show various tradeoffs. Finally, we provide preliminary experimental results which suggest that our algorithms are of interest in practice.", acknowledgement = ack-nhfb, } @InProceedings{Meng:2013:LDS, author = "Xiangrui Meng and Michael W. Mahoney", title = "Low-distortion subspace embeddings in input-sparsity time and applications to robust linear regression", crossref = "ACM:2013:SPF", pages = "91--100", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488621", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Low-distortion embeddings are critical building blocks for developing random sampling and random projection algorithms for common linear algebra problems. We show that, given a matrix $ A \in R^{n x d} $ with $ n \gg d $ and $ a p \in [1, 2) $, with a constant probability, we can construct a low-distortion embedding matrix $ \Pi \in R^{O({\rm poly}(d)) x n} $ that embeds $ A_p $, the $ l_p $ subspace spanned by $A$'s columns, into $ (R^{O({\rm poly}(d))}, | \cdot |_p) $; the distortion of our embeddings is only $ O({\rm poly}(d)) $, and we can compute $ \Pi A $ in $ O(n n z(A)) $ time, i.e., input-sparsity time. Our result generalizes the input-sparsity time $ l_2 $ subspace embedding by Clarkson and Woodruff [STOC'13]; and for completeness, we present a simpler and improved analysis of their construction for $ l_2 $. These input-sparsity time $ l_p $ embeddings are optimal, up to constants, in terms of their running time; and the improved running time propagates to applications such as $ (1 p m \epsilon) $-distortion $ l_p $ subspace embedding and relative-error $ l_p $ regression. For $ l_2 $, we show that a $ (1 + \epsilon) $-approximate solution to the $ l_2 $ regression problem specified by the matrix $A$ and a vector $ b \in R^n $ can be computed in $ O(n n z(A) + d^3 \log (d / \epsilon) / \epsilon^2) $ time; and for $ l_p $, via a subspace-preserving sampling procedure, we show that a $ (1 p m \epsilon) $-distortion embedding of $ A_p $ into $ R^{O({\rm poly}(d))} $ can be computed in $ O(n n z(A) \cdot \log n) $ time, and we also show that a $ (1 + \epsilon) $-approximate solution to the $ l_p $ regression problem $ \min_{x \in R^d} |A x - b|_p $ can be computed in $ O(n n z(A) \cdot \log n + {\rm poly}(d) \log (1 / \epsilon) / \epsilon^2) $ time. Moreover, we can also improve the embedding dimension or equivalently the sample size to $ O(d^{3 + p / 2} \log (1 / \epsilon) / \epsilon^2) $ without increasing the complexity.", acknowledgement = ack-nhfb, } @InProceedings{Nelson:2013:SLB, author = "Jelani Nelson and Huy L. Nguyen", title = "Sparsity lower bounds for dimensionality reducing maps", crossref = "ACM:2013:SPF", pages = "101--110", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488622", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We give near-tight lower bounds for the sparsity required in several dimensionality reducing linear maps. First, consider the Johnson--Lindenstrauss (JL) lemma which states that for any set of $n$ vectors in $ R^d $ there is an $ A \in R^{m \times d} $ with $ m = O(\epsilon^{-2} \log n) $ such that mapping by $A$ preserves the pairwise Euclidean distances up to a $ 1 \pm \epsilon $ factor. We show there exists a set of $n$ vectors such that any such $A$ with at most $s$ non-zero entries per column must have $ s = \Omega (\epsilon^{-1} \log n / \log (1 / \epsilon)) $ if $ m < O(n / \log (1 / \epsilon)) $. This improves the lower bound of $ \Omega (\min \{ \epsilon^{-2}, \epsilon^{-1} \sqrt (\log_m d) \}) $ by [Dasgupta-Kumar-Sarlos, STOC 2010], which only held against the stronger property of distributional JL, and only against a certain restricted class of distributions. Meanwhile our lower bound is against the JL lemma itself, with no restrictions. Our lower bound matches the sparse JL upper bound of [Kane-Nelson, SODA 2012] up to an $ O(\log (1 / \epsilon)) $ factor. Next, we show that any $ m \times n $ matrix with the $k$-restricted isometry property (RIP) with constant distortion must have $ \Omega (k \log (n / k)) $ non-zeroes per column if $ m = O(k \log (n / k)) $, the optimal number of rows for RIP, and $ k < n / \polylog n $. This improves the previous lower bound of $ \Omega (\min \{ k, n / m \}) $ by [Chandar, 2010] and shows that for most $k$ it is impossible to have a sparse RIP matrix with an optimal number of rows. Both lower bounds above also offer a tradeoff between sparsity and the number of rows. Lastly, we show that any oblivious distribution over subspace embedding matrices with 1 non-zero per column and preserving distances in a $d$ dimensional-subspace up to a constant factor must have at least $ \Omega (d^2) $ rows. This matches an upper bound in [Nelson-Nguy{\^e}n, arXiv abs/1211.1002] and shows the impossibility of obtaining the best of both of constructions in that work, namely 1 non-zero per column and $ d \cdot \polylog d $ rows.", acknowledgement = ack-nhfb, } @InProceedings{Bitansky:2013:RCB, author = "Nir Bitansky and Ran Canetti and Alessandro Chiesa and Eran Tromer", title = "Recursive composition and bootstrapping for {SNARKS} and proof-carrying data", crossref = "ACM:2013:SPF", pages = "111--120", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488623", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Succinct non-interactive arguments of knowledge (SNARKs) enable verifying NP statements with complexity that is essentially independent of that required for classical NP verification. In particular, they provide strong solutions to the problem of verifiably delegating computation. We construct the first fully-succinct publicly-verifiable SNARK. To do that, we first show how to ``bootstrap'' any SNARK that requires expensive preprocessing to obtain a SNARK that does not, while preserving public verifiability. We then apply this transformation to known SNARKs with preprocessing. Moreover, the SNARK we construct only requires of the prover time and space that are essentially the same as that required for classical NP verification. Our transformation assumes only collision-resistant hashing; curiously, it does not rely on PCPs. We also show an analogous transformation for privately-verifiable SNARKs, assuming fully-homomorphic encryption. At the heart of our transformations is a technique for recursive composition of SNARKs. This technique uses in an essential way the proof-carrying data (PCD) framework, which extends SNARKs to the setting of distributed networks of provers and verifiers. Concretely, to bootstrap a given SNARK, we recursively compose the SNARK to obtain a ``weak'' PCD system for shallow distributed computations, and then use the PCD framework to attain stronger notions of SNARKs and PCD systems.", acknowledgement = ack-nhfb, } @InProceedings{Hardt:2013:HRL, author = "Moritz Hardt and David P. Woodruff", title = "How robust are linear sketches to adaptive inputs?", crossref = "ACM:2013:SPF", pages = "121--130", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488624", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Linear sketches are powerful algorithmic tools that turn an $n$-dimensional input into a concise lower-dimensional representation via a linear transformation. Such sketches have seen a wide range of applications including norm estimation over data streams, compressed sensing, and distributed computing. In almost any realistic setting, however, a linear sketch faces the possibility that its inputs are correlated with previous evaluations of the sketch. Known techniques no longer guarantee the correctness of the output in the presence of such correlations. We therefore ask: Are linear sketches inherently non-robust to adaptively chosen inputs? We give a strong affirmative answer to this question. Specifically, we show that no linear sketch approximates the Euclidean norm of its input to within an arbitrary multiplicative approximation factor on a polynomial number of adaptively chosen inputs. The result remains true even if the dimension of the sketch is d=n-o(n) and the sketch is given unbounded computation time. Our result is based on an algorithm with running time polynomial in d that adaptively finds a distribution over inputs on which the sketch is incorrect with constant probability. Our result implies several corollaries for related problems including l$_p$ -norm estimation and compressed sensing. Notably, we resolve an open problem in compressed sensing regarding the feasibility of l$_2$ /l$_2$ -recovery guarantees in presence of computationally bounded adversaries.", acknowledgement = ack-nhfb, } @InProceedings{Bohm:2013:EDO, author = "Stanislav B{\"o}hm and Stefan G{\"o}ller and Petr Jancar", title = "Equivalence of deterministic one-counter automata is {NL}-complete", crossref = "ACM:2013:SPF", pages = "131--140", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488626", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We prove that language equivalence of deterministic one-counter automata is NL-complete. This improves the superpolynomial time complexity upper bound shown by Valiant and Paterson in 1975. Our main contribution is to prove that two deterministic one-counter automata are inequivalent if and only if they can be distinguished by a word of length polynomial in the size of the two input automata.", acknowledgement = ack-nhfb, } @InProceedings{Burgisser:2013:ELB, author = "Peter B{\"u}rgisser and Christian Ikenmeyer", title = "Explicit lower bounds via geometric complexity theory", crossref = "ACM:2013:SPF", pages = "141--150", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488627", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We prove the lower bound $ R (M_m) \geq 3 / 2 m^2 - 2 $ on the border rank of $ m \times m $ matrix multiplication by exhibiting explicit representation theoretic (occurrence) obstructions in the sense of Mulmuley and Sohoni's geometric complexity theory (GCT) program. While this bound is weaker than the one recently obtained by Landsberg and Ottaviani, these are the first significant lower bounds obtained within the GCT program. Behind the proof is an explicit description of the highest weight vectors in Sym$^d \otimes^3 (C^n)*$ in terms of combinatorial objects, called obstruction designs. This description results from analyzing the process of polarization and Schur--Weyl duality.", acknowledgement = ack-nhfb, } @InProceedings{Braverman:2013:IEC, author = "Mark Braverman and Ankit Garg and Denis Pankratov and Omri Weinstein", title = "From information to exact communication", crossref = "ACM:2013:SPF", pages = "151--160", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488628", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We develop a new local characterization of the zero-error information complexity function for two-party communication problems, and use it to compute the exact internal and external information complexity of the 2-bit AND function: $ {\rm IC}({\rm AND}, 0) = C_{\wedge } \cong 1.4923 $ bits, and $ {\rm IC}^{ext} ({\rm AND}, 0) = \log_2 3 \cong 1.5839 $ bits. This leads to a tight (upper and lower bound) characterization of the communication complexity of the set intersection problem on subsets of $ \{ 1, \ldots {}, n \} $ (the player are required to compute the intersection of their sets), whose randomized communication complexity tends to $ C_{\wedge } \cdot n \pm o(n) $ as the error tends to zero. The information-optimal protocol we present has an infinite number of rounds. We show this is necessary by proving that the rate of convergence of the r-round information cost of AND to $ {\rm IC}({\rm AND}, 0) = C_{\wedge } $ behaves like $ \Theta (1 / r^2) $, i.e. that the $r$-round information complexity of AND is $ C_\wedge + \Theta (1 / r^2) $. We leverage the tight analysis obtained for the information complexity of AND to calculate and prove the exact communication complexity of the set disjointness function $ {\rm Disj}_n (X, Y) = - v_{i = 1}^n {\rm AND}(x_i, y_i) $ with error tending to $0$, which turns out to be $ = C_{\rm DISJ} \cdot n \pm o(n) $, where $ C_{\rm DISJ} \cong 0.4827 $. Our rate of convergence results imply that an asymptotically optimal protocol for set disjointness will have to use $ \omega (1) $ rounds of communication, since every $r$-round protocol will be sub-optimal by at least $ \Omega (n / r^2) $ bits of communication. We also obtain the tight bound of $ 2 / \ln 2 k \pm o(k) $ on the communication complexity of disjointness of sets of size $ \leq k $. An asymptotic bound of $ \Theta (k) $ was previously shown by Hastad and Wigderson.", acknowledgement = ack-nhfb, } @InProceedings{Braverman:2013:ICA, author = "Mark Braverman and Ankur Moitra", title = "An information complexity approach to extended formulations", crossref = "ACM:2013:SPF", pages = "161--170", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488629", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We prove an unconditional lower bound that any linear program that achieves an $ O(n^{1 - \epsilon }) $ approximation for clique has size $ 2^{ \Omega (n \epsilon)} $. There has been considerable recent interest in proving unconditional lower bounds against any linear program. Fiorini et al. proved that there is no polynomial sized linear program for traveling salesman. Braun et al. proved that there is no polynomial sized $ O(n^{1 / 2 - \epsilon }) $-approximate linear program for clique. Here we prove an optimal and unconditional lower bound against linear programs for clique that matches Hastad's celebrated hardness result. Interestingly, the techniques used to prove such lower bounds have closely followed the progression of techniques used in communication complexity. Here we develop an information theoretic framework to approach these questions, and we use it to prove our main result. Also we resolve a related question: How many bits of communication are needed to get $ \epsilon $ advantage over random guessing for disjointness? Kalyanasundaram and Schnitger proved that a protocol that gets constant advantage requires $ \Omega (n) $ bits of communication. This result in conjunction with amplification implies that any protocol that gets $ \epsilon $-advantage requires $ \Omega (\epsilon^2 n) $ bits of communication. Here we improve this bound to $ \Omega (\epsilon n) $, which is optimal for any $ \epsilon > 0 $.", acknowledgement = ack-nhfb, } @InProceedings{Komargodski:2013:ACL, author = "Ilan Komargodski and Ran Raz", title = "Average-case lower bounds for formula size", crossref = "ACM:2013:SPF", pages = "171--180", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488630", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We give an explicit function $ h : \{ 0, 1 \}^n \to \{ 0, 1 \} $ such that any deMorgan formula of size $ O(n^{2.499}) $ agrees with $h$ on at most $ 1 / 2 + \epsilon $ fraction of the inputs, where $ \epsilon $ is exponentially small (i.e. $ \epsilon = 2^{-n \Omega (1)} $ ). We also show, using the same technique, that any boolean formula of size $ O(n^{1.999}) $ over the complete basis, agrees with $h$ on at most $ 1 / 2 + \epsilon $ fraction of the inputs, where $ \epsilon $ is exponentially small (i.e. $ \epsilon = 2^{-vn \Omega (1)} $ ). Our construction is based on Andreev's $ \Omega (n^{2.5 - o(1)}) $ formula size lower bound that was proved for the case of exact computation.", acknowledgement = ack-nhfb, } @InProceedings{Chen:2013:CNM, author = "Xi Chen and Dimitris Paparas and Mihalis Yannakakis", title = "The complexity of non-monotone markets", crossref = "ACM:2013:SPF", pages = "181--190", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488632", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We introduce the notion of non-monotone utilities, which covers a wide variety of utility functions in economic theory. We show that it is PPAD-hard to compute an approximate Arrow--Debreu market equilibrium in markets with linear and non-monotone utilities. Building on this result, we settle the long-standing open problem regarding the computation of an approximate Arrow--Debreu market equilibrium in markets with CES utilities, by proving that it is PPAD-complete when the Constant Elasticity of Substitution parameter, $ \rho $, is any constant less than $ - 1 $.", acknowledgement = ack-nhfb, } @InProceedings{Cheung:2013:TBG, author = "Yun Kuen Cheung and Richard Cole and Nikhil Devanur", title = "Tatonnement beyond gross substitutes?: gradient descent to the rescue", crossref = "ACM:2013:SPF", pages = "191--200", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488633", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Tatonnement is a simple and natural rule for updating prices in Exchange (Arrow--Debreu) markets. In this paper we define a class of markets for which tatonnement is equivalent to gradient descent. This is the class of markets for which there is a convex potential function whose gradient is always equal to the negative of the excess demand and we call it Convex Potential Function (CPF) markets. We show the following results. CPF markets contain the class of Eisenberg Gale (EG) markets, defined previously by Jain and Vazirani. The subclass of CPF markets for which the demand is a differentiable function contains exactly those markets whose demand function has a symmetric negative semi-definite Jacobian. We define a family of continuous versions of tatonnement based on gradient descent using a Bregman divergence. As we show, all processes in this family converge to an equilibrium for any CPF market. This is analogous to the classic result for markets satisfying the Weak Gross Substitutes property. A discrete version of tatonnement converges toward the equilibrium for the following markets of complementary goods; its convergence rate for these settings is analyzed using a common potential function. Fisher markets in which all buyers have Leontief utilities. The tatonnement process reduces the distance to the equilibrium, as measured by the potential function, to an $ \epsilon $ fraction of its initial value in $ O(1 / \epsilon) $ rounds of price updates. Fisher markets in which all buyers have complementary CES utilities. Here, the distance to the equilibrium is reduced to an $ \epsilon $ fraction of its initial value in $ O(\log (1 / \epsilon)) $ rounds of price updates. This shows that tatonnement converges for the entire range of Fisher markets when buyers have complementary CES utilities, in contrast to prior work, which could analyze only the substitutes range, together with a small portion of the complementary range.", acknowledgement = ack-nhfb, } @InProceedings{Feldman:2013:SAA, author = "Michal Feldman and Hu Fu and Nick Gravin and Brendan Lucier", title = "Simultaneous auctions are (almost) efficient", crossref = "ACM:2013:SPF", pages = "201--210", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488634", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Simultaneous item auctions are simple and practical procedures for allocating items to bidders with potentially complex preferences. In a simultaneous auction, every bidder submits independent bids on all items simultaneously. The allocation and prices are then resolved for each item separately, based solely on the bids submitted on that item. We study the efficiency of Bayes-Nash equilibrium (BNE) outcomes of simultaneous first- and second-price auctions when bidders have complement-free (a.k.a. subadditive) valuations. While it is known that the social welfare of every pure Nash equilibrium (NE) constitutes a constant fraction of the optimal social welfare, a pure NE rarely exists, and moreover, the full information assumption is often unrealistic. Therefore, quantifying the welfare loss in Bayes-Nash equilibria is of particular interest. Previous work established a logarithmic bound on the ratio between the social welfare of a BNE and the expected optimal social welfare in both first-price auctions (Hassidim et al., 2011) and second-price auctions (Bhawalkar and Roughgarden, 2011), leaving a large gap between a constant and a logarithmic ratio. We introduce a new proof technique and use it to resolve both of these gaps in a unified way. Specifically, we show that the expected social welfare of any BNE is at least 1/2 of the optimal social welfare in the case of first-price auctions, and at least 1/4 in the case of second-price auctions.", acknowledgement = ack-nhfb, } @InProceedings{Syrgkanis:2013:CEM, author = "Vasilis Syrgkanis and Eva Tardos", title = "Composable and efficient mechanisms", crossref = "ACM:2013:SPF", pages = "211--220", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488635", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We initiate the study of efficient mechanism design with guaranteed good properties even when players participate in multiple mechanisms simultaneously or sequentially. We define the class of smooth mechanisms, related to smooth games defined by Roughgarden, that can be thought of as mechanisms that generate approximately market clearing prices. We show that smooth mechanisms result in high quality outcome both in equilibrium and in learning outcomes in the full information setting, as well as in Bayesian equilibrium with uncertainty about participants. Our main result is to show that smooth mechanisms compose well: smoothness locally at each mechanism implies global efficiency. For mechanisms where good performance requires that bidders do not bid above their value, we identify the notion of a weakly smooth mechanism. Weakly smooth mechanisms, such as the Vickrey auction, are approximately efficient under the no-overbidding assumption, and the weak smoothness property is also maintained by composition. In most of the paper we assume participants have quasi-linear valuations. We also extend some of our results to settings where participants have budget constraints.", acknowledgement = ack-nhfb, } @InProceedings{Goyal:2013:NBB, author = "Vipul Goyal", title = "Non-black-box simulation in the fully concurrent setting", crossref = "ACM:2013:SPF", pages = "221--230", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488637", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We present a new zero-knowledge argument protocol by relying on the non-black-box simulation technique of Barak (FOCS'01). Similar to the protocol of Barak, ours is public-coin, is based on the existence of collision-resistant hash functions, and, is not based on ``rewinding techniques'' but rather uses non-black-box simulation. However in contrast to the protocol of Barak, our protocol is secure even if there are any unbounded (polynomial) number of concurrent sessions. This gives us the first construction of public-coin concurrent zero-knowledge. Prior to our work, Pass, Tseng and Wikstrom (SIAM J. Comp. 2011) had shown that using black-box simulation, getting a construction for even public-coin parallel zero-knowledge is impossible. A public-coin concurrent zero-knowledge protocol directly implies the existence of a concurrent resettably-sound zero-knowledge protocol. This is an improvement over the corresponding construction of Deng, Goyal and Sahai (FOCS'09) which was based on stronger assumptions. Furthermore, this also directly leads to an alternative (and arguable cleaner) construction of a simultaneous resettable zero-knowledge argument system. An important feature of our protocol is the existence of a ``straight-line'' simulator. This gives a fundamentally different tool for constructing concurrently secure computation protocols (for functionalities even beyond zero-knowledge). The round complexity of our protocol is $ n^\epsilon $ (for any constant $ \epsilon > 0 $ ), and, the simulator runs in strict polynomial time. The main technique behind our construction is purely combinatorial in nature.", acknowledgement = ack-nhfb, } @InProceedings{Chung:2013:NBB, author = "Kai-Min Chung and Rafael Pass and Karn Seth", title = "Non-black-box simulation from one-way functions and applications to resettable security", crossref = "ACM:2013:SPF", pages = "231--240", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488638", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "The simulation paradigm, introduced by Goldwasser, Micali and Rackoff, is of fundamental importance to modern cryptography. In a breakthrough work from 2001, Barak (FOCS'01) introduced a novel non-black-box simulation technique. This technique enabled the construction of new cryptographic primitives, such as resettably-sound zero-knowledge arguments, that cannot be proven secure using just black-box simulation techniques. The work of Barak and its follow-ups, however, all require stronger cryptographic hardness assumptions than the minimal assumption of one-way functions. In this work, we show how to perform non-black-box simulation assuming just the existence of one-way functions. In particular, we demonstrate the existence of a constant-round resettably-sound zero-knowledge argument based only on the existence of one-way functions. Using this technique, we determine necessary and sufficient assumptions for several other notions of resettable security of zero-knowledge proofs. An additional benefit of our approach is that it seemingly makes practical implementations of non-black-box zero-knowledge viable.", acknowledgement = ack-nhfb, } @InProceedings{Bitansky:2013:IAO, author = "Nir Bitansky and Omer Paneth", title = "On the impossibility of approximate obfuscation and applications to resettable cryptography", crossref = "ACM:2013:SPF", pages = "241--250", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488639", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "The traditional notion of program obfuscation requires that an obfuscation \char`{\~P}rog of a program Prog computes the exact same function as Prog, but beyond that, the code of \char`{\~P}rog should not leak any information about Prog. This strong notion of virtual black-box security was shown by Barak et al. (CRYPTO 2001) to be impossible to achieve, for certain unobfuscatable function families. The same work raised the question of approximate obfuscation, where the obfuscated \char`{\~P}rog is only required to approximate Prog; that is, \char`{\~P}rog only agrees with Prog with high enough probability on some input distribution. We show that, assuming trapdoor permutations, there exist families of robust unobfuscatable functions for which even approximate obfuscation is impossible. Specifically, obfuscation is impossible even if the obfuscated \char`{\~P}rog is only required to agree with Prog with probability slightly more than 1/2, on a uniformly sampled input (below 1/2-agreement, the function obfuscated by \char`{\~P}rog is not uniquely defined). Additionally, assuming only one-way functions, we rule out approximate obfuscation where \char`{\~P}rog may output bot with probability close to $1$, but otherwise must agree with Prog. We demonstrate the power of robust unobfuscatable functions by exhibiting new implications to resettable protocols. Concretely, we reduce the assumptions required for resettably-sound zero-knowledge to one-way functions, as well as reduce round-complexity. We also present a new simplified construction of a simultaneously-resettable zero-knowledge protocol. Finally, we construct a three-message simultaneously-resettable witness-indistinguishable argument of knowledge (with a non-black-box knowledge extractor). Our constructions use a new non-black-box simulation technique that is based on a special kind of ``resettable slots''. These slots are useful for a non-black-box simulator, but not for a resetting prover.", acknowledgement = ack-nhfb, } @InProceedings{Miles:2013:SCG, author = "Eric Miles and Emanuele Viola", title = "Shielding circuits with groups", crossref = "ACM:2013:SPF", pages = "251--260", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488640", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We show how to efficiently compile any given circuit C into a leakage-resistant circuit C' such that any function on the wires of C' that leaks information during a computation C'(x) yields advantage in computing the product of |C'|$^{ \Omega (1)}$ elements of the alternating group A$_u$. In combination with new compression bounds for A$_u$ products, also obtained here, C' withstands leakage from virtually any class of functions against which average-case lower bounds are known. This includes communication protocols, and A$ C^0 $ circuits augmented with few arbitrary symmetric gates. If N$ C^1 $ ' T$ C^0 $ then the construction resists T$ C^0 $ leakage as well. We also conjecture that our construction resists N$ C^1 $ leakage. In addition, we extend the construction to the multi-query setting by relying on a simple secure hardware component. We build on Barrington's theorem [JCSS '89] and on the previous leakage-resistant constructions by Ishai et al. [Crypto '03] and Faust et al. [Eurocrypt '10]. Our construction exploits properties of A$_u$ beyond what is sufficient for Barrington's theorem.", acknowledgement = ack-nhfb, } @InProceedings{Babai:2013:QTC, author = "Laszlo Babai and John Wilmes", title = "Quasipolynomial-time canonical form for {Steiner} designs", crossref = "ACM:2013:SPF", pages = "261--270", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488642", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "A Steiner 2-design is a finite geometry consisting of a set of ``points'' together with a set of ``lines'' (subsets of points of uniform cardinality) such that each pair of points belongs to exactly one line. In this paper we analyse the individualization/refinement heuristic and conclude that after individualizing $ O(\log n) $ points (assigning individual colors to them), the refinement process gives each point an individual color. The following consequences are immediate: (a) isomorphism of Steiner 2-designs can be tested in $ n^{O(\log n)} $ time, where $n$ is the number of lines; (b) a canonical form of Steiner 2-designs can be computed within the same time bound; (c) all isomorphisms between two Steiner 2-designs can be listed within the same time bound; (d) the number of automorphisms of a Steiner 2-design is at most n$^{O(\log n)}$ (a fact of interest to finite geometry and group theory.) The best previous bound in each of these four statements was moderately exponential, $ \exp (\tilde O(n^{1 / 4})) $ (Spielman, STOC'96). Our result removes an exponential bottleneck from Spielman's analysis of the Graph Isomorphism problem for strongly regular graphs. The results extend to Steiner $t$-designs for all $ t \geq 2 $. Strongly regular (s.r.) graphs have been known as hard cases for graph isomorphism testing; the best previously known bound for this case is moderately exponential, $ \exp (\tilde O(n^{1 / 3})) $ where $n$ is the number of vertices (Spielman, STOC'96). Line graphs of Steiner $2$-designs enter as a critical subclass via Neumaier's 1979 classification of s.r. graphs. Previously, $ n^{O(\log n)} $ isomorphism testing and canonical forms for Steiner 2-designs was known for the case when the lines of the Steiner 2-design have bounded length (Babai and Luks, STOC'83). That paper relied on Luks's group-theoretic divide-and-conquer algorithms and did not yield a subexponential bound on the number of automorphisms. To analyse the individualization/refinement heuristic, we develop a new structure theory of Steiner 2-designs based on the analysis of controlled growth and on an addressing scheme that produces a hierarchy of increasing sets of pairwise independent, uniformly distributed points. This scheme represents a new expression of the structural homogeneity of Steiner 2-designs that allows applications of the second moment method. We also address the problem of reconstruction of Steiner 2-designs from their line-graphs beyond the point of unique reconstructability, in a manner analogous to list-decoding, and as a consequence achieve an $ \exp (\tilde O(n^{1 / 6})) $ bound for isomorphism testing for this class of s.r. graphs. Results, essentially identical to our main results, were obtained simultaneously by Xi Chen, Xiaorui Sun, and Shang-Hua Teng, building on a different philosophy and combinatorial structure theory than the present paper. They do not claim an analysis of the individualization/refinement algorithm but of a more complex combinatorial algorithm. We comment on how this paper fits into the overall project of improved isomorphism testing for strongly regular graphs (the ultimate goal being subexponential $ \exp (n^{o(1)}) $ time). In the remaining cases we need to deal with s.r. graphs satisfying ``Neumaier's claw bound,'' permitting the use of a separate set of asymptotic structural tools. In joint work (in progress) with Chen, Sun, and Teng, we address that case and have already pushed the overall bound below $ \exp (\tilde O(n^{1 / 4})) $ The present paper is a methodologically distinct and stand-alone part of the overall project.", acknowledgement = ack-nhfb, } @InProceedings{Chen:2013:MSD, author = "Xi Chen and Xiaorui Sun and Shang-Hua Teng", title = "Multi-stage design for quasipolynomial-time isomorphism testing of {Steiner} $2$-systems", crossref = "ACM:2013:SPF", pages = "271--280", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488643", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "A standard heuristic for testing graph isomorphism is to first assign distinct labels to a small set of vertices of an input graph, and then propagate to create new vertex labels across the graph, aiming to assign distinct and isomorphism-invariant labels to all vertices in the graph. This is usually referred to as the individualization/refinement method for canonical labeling of graphs. We present a quasipolynomial-time algorithm for isomorphism testing of Steiner 2-systems. A Steiner 2-system consists of points and lines, where each line passes the same number of points and each pair of points uniquely determines a line. Each Steiner 2-system induces a Steiner graph, in which vertices represent lines and edges represent intersections of lines. Steiner graphs are an important subfamily of strongly regular graphs whose isomorphism testing has challenged researchers for years. Inspired by both the individualization/refinement method and the previous analyses of Babai and Spielman, we consider an extended framework for isomorphism testing of Steiner 2-systems, in which we use a small set of randomly chosen points and lines to build isomorphism-invariant multi-stage combinatorial structures that are sufficient to distinguish all pairs of points of a Steiner 2-system. Applying this framework, we show that isomorphism of Steiner 2-systems with $n$ lines can be tested in time $\smash n^{O(\log n)}$, improving the previous best bound of $ \smash \exp (\tilde O(n^{1 / 4})) $ by Spielman. Before our result, quasipolynomial-time isomorphism testing was only known for the case when the line size is polylogarithmic, as shown by Babai and Luks. A result essentially identical to ours was obtained simultaneously by Laszlo Babai and John Wilmes. They performed a direct analysis of the individualization/refinement method, building on a different philosophy and combinatorial structure theory. We comment on how this paper fits into the overall project of improved isomorphism testing for strongly regular graphs (the ultimate goal being subexponential $ \exp (n^{o(1)}) $ time). In the remaining cases, we only need to deal with strongly regular graphs satisfying ``Neumaier's claw bound,'' permitting the use of a separate set of asymptotic structural tools. In joint work (in progress) with Babai and Wilmes, we address that case and have already pushed the overall bound below $ \smash \exp (\tilde O(n^{1 / 4})) $. The present paper is a methodologically distinct and stand-alone part of the overall project.", acknowledgement = ack-nhfb, } @InProceedings{Gupta:2013:SCB, author = "Anupam Gupta and Kunal Talwar and David Witmer", title = "Sparsest cut on bounded treewidth graphs: algorithms and hardness results", crossref = "ACM:2013:SPF", pages = "281--290", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488644", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We give a 2-approximation algorithm for the non-uniform Sparsest Cut problem that runs in time $ n^{O(k)} $, where $k$ is the treewidth of the graph. This improves on the previous $ 2^{2 k} $ approximation in time $ \poly (n) 2^{O(k)} $ due to Chlamtac et al. [18]. To complement this algorithm, we show the following hardness results: If the non-uniform Sparsest Cut has a $ \rho $-approximation for series-parallel graphs (where $ \rho \geq 1 $ ), then the MaxCut problem has an algorithm with approximation factor arbitrarily close to $ 1 / \rho $. Hence, even for such restricted graphs (which have treewidth 2), the Sparsest Cut problem is NP-hard to approximate better than $ 17 / 16 - \epsilon $ for $ \epsilon > 0 $; assuming the Unique Games Conjecture the hardness becomes $ 1 / \alpha_{GW} - \epsilon $. For graphs with large (but constant) treewidth, we show a hardness result of $ 2 - \epsilon $ assuming the Unique Games Conjecture. Our algorithm rounds a linear program based on (a subset of) the Sherali--Adams lift of the standard Sparsest Cut LP. We show that even for treewidth-2 graphs, the LP has an integrality gap close to 2 even after polynomially many rounds of Sherali--Adams. Hence our approach cannot be improved even on such restricted graphs without using a stronger relaxation.", acknowledgement = ack-nhfb, } @InProceedings{Chekuri:2013:LTG, author = "Chandra Chekuri and Julia Chuzhoy", title = "Large-treewidth graph decompositions and applications", crossref = "ACM:2013:SPF", pages = "291--300", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488645", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Treewidth is a graph parameter that plays a fundamental role in several structural and algorithmic results. We study the problem of decomposing a given graph $G$ into node-disjoint subgraphs, where each subgraph has sufficiently large treewidth. We prove two theorems on the tradeoff between the number of the desired subgraphs h, and the desired lower bound r on the treewidth of each subgraph. The theorems assert that, given a graph $G$ with treewidth $k$, a decomposition with parameters $ h, r $ is feasible whenever $ h r^2 \leq k / \polylog (k) $, or $ h^3 r \leq k / \polylog (k) $ holds. We then show a framework for using these theorems to bypass the well-known Grid-Minor Theorem of Robertson and Seymour in some applications. In particular, this leads to substantially improved parameters in some Erd{\H{o}}s--Posa-type results, and faster algorithms for some fixed-parameter tractable problems.", acknowledgement = ack-nhfb, } @InProceedings{Cygan:2013:FHC, author = "Marek Cygan and Stefan Kratsch and Jesper Nederlof", title = "Fast {Hamiltonicity} checking via bases of perfect matchings", crossref = "ACM:2013:SPF", pages = "301--310", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488646", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "For an even integer $ t \geq 2 $, the Matching Connectivity matrix $ H_t $ is a matrix that has rows and columns both labeled by all perfect matchings of the complete graph $ K_t $ on $t$ vertices; an entry $ H_t [M_1, M_2] $ is $1$ if $ M_1 \cup M_2 $ is a Hamiltonian cycle and $0$ otherwise. Motivated by the computational study of the Hamiltonicity problem, we present three results on the structure of $ H_t $: We first show that $ H_t $ has rank exactly $ 2^{t / 2 - 1} $ over GF(2) via an appropriate factorization that explicitly provides families of matchings $ X_t $ forming bases for $ H_t $. Second, we show how to quickly change representation between such bases. Third, we notice that the sets of matchings $ X_t $ induce permutation matrices within $ H_t $. We use the factorization to derive an $ 1.888^n n^{O(1)} $ time Monte Carlo algorithm that solves the Hamiltonicity problem in directed bipartite graphs. Our algorithm as well counts the number of Hamiltonian cycles modulo two in directed bipartite or undirected graphs in the same time bound. Moreover, we use the fast basis change algorithm from the second result to present a Monte Carlo algorithm that given an undirected graph on $n$ vertices along with a path decomposition of width at most pw decides Hamiltonicity in $ (2 + \sqrt 2)^{pw} n^{O(1)} $ time. Finally, we use the third result to show that for every $ \epsilon > 0 $ this cannot be improved to $ (2 + \sqrt 2 - \epsilon)^{pw} n^{O(1)} $ time unless the Strong Exponential Time Hypothesis fails, i.e., a faster algorithm for this problem would imply the breakthrough result of an $ O((2 - \epsilon ')^n) $ time algorithm for CNF-Sat.", acknowledgement = ack-nhfb, } @InProceedings{Keevash:2013:PTP, author = "Peter Keevash and Fiachra Knox and Richard Mycroft", title = "Polynomial-time perfect matchings in dense hypergraphs", crossref = "ACM:2013:SPF", pages = "311--320", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488647", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Let H be a $k$-graph on $n$ vertices, with minimum codegree at least n/k + cn for some fixed c > 0. In this paper we construct a polynomial-time algorithm which finds either a perfect matching in H or a certificate that none exists. This essentially solves a problem of Karpinski, Rucinski and Szymanska, who previously showed that this problem is NP-hard for a minimum codegree of n/k --- cn. Our algorithm relies on a theoretical result of independent interest, in which we characterise any such hypergraph with no perfect matching using a family of lattice-based constructions.", acknowledgement = ack-nhfb, } @InProceedings{Agrawal:2013:QPH, author = "Manindra Agrawal and Chandan Saha and Nitin Saxena", title = "Quasi-polynomial hitting-set for set-depth-{$ \Delta $} formulas", crossref = "ACM:2013:SPF", pages = "321--330", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488649", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We call a depth-4 formula $C$ set-depth-4 if there exists a (unknown) partition $ X_1 \sqcup \cdots \sqcup X_d $ of the variable indices $ [n] $ that the top product layer respects, i.e. $ C({{\rm term} x}) = \Sigma_{i = 1}^k \prod_{j = 1}^d f_{i, j} ({{\rm term} x}_{X j}) $, where $ f_{i, j} $ is a sparse polynomial in $ F[{{\rm term} x}_{X j}] $. Extending this definition to any depth --- we call a depth-$D$ formula $C$ (consisting of alternating layers of $ \Sigma $ and $ \Pi $ gates, with a $ \Sigma $-gate on top) a set-depth-$D$ formula if every $ \Pi $-layer in $C$ respects a (unknown) partition on the variables; if $D$ is even then the product gates of the bottom-most $ \Pi $-layer are allowed to compute arbitrary monomials. In this work, we give a hitting-set generator for set-depth-$D$ formulas (over any field) with running time polynomial in $ \exp ((D^2 \log s)^{\Delta - 1}) $, where $s$ is the size bound on the input set-depth-$D$ formula. In other words, we give a quasi-polynomial time blackbox polynomial identity test for such constant-depth formulas. Previously, the very special case of $ D = 3 $ (also known as set-multilinear depth-3 circuits) had no known sub-exponential time hitting-set generator. This was declared as an open problem by Shpilka {\&} Yehudayoff (FnT-TCS 2010); the model being first studied by Nisan {\&} Wigderson (FOCS 1995) and recently by Forbes {\&} Shpilka (STOC 2012 {\&} ECCC TR12-115). Our work settles this question, not only for depth-3 but, up to depth $ \epsilon \log s / \log \log s $, for a fixed constant $ \epsilon < 1 $. The technique is to investigate depth-$D$ formulas via depth-$ (D - 1) $ formulas over a Hadamard algebra, after applying a shift' on the variables. We propose a new algebraic conjecture about the low-support rank-concentration in the latter formulas, and manage to prove it in the case of set-depth-$D$ formulas.", acknowledgement = ack-nhfb, } @InProceedings{Hardt:2013:BWC, author = "Moritz Hardt and Aaron Roth", title = "Beyond worst-case analysis in private singular vector computation", crossref = "ACM:2013:SPF", pages = "331--340", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488650", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We consider differentially private approximate singular vector computation. Known worst-case lower bounds show that the error of any differentially private algorithm must scale polynomially with the dimension of the singular vector. We are able to replace this dependence on the dimension by a natural parameter known as the coherence of the matrix that is often observed to be significantly smaller than the dimension both theoretically and empirically. We also prove a matching lower bound showing that our guarantee is nearly optimal for every setting of the coherence parameter. Notably, we achieve our bounds by giving a robust analysis of the well-known power iteration algorithm, which may be of independent interest. Our algorithm also leads to improvements in worst-case settings and to better low-rank approximations in the spectral norm.", acknowledgement = ack-nhfb, } @InProceedings{Hsu:2013:DPA, author = "Justin Hsu and Aaron Roth and Jonathan Ullman", title = "Differential privacy for the analyst via private equilibrium computation", crossref = "ACM:2013:SPF", pages = "341--350", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488651", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We give new mechanisms for answering exponentially many queries from multiple analysts on a private database, while protecting dif- ferential privacy both for the individuals in the database and for the analysts. That is, our mechanism's answer to each query is nearly insensitive to changes in the queries asked by other analysts. Our mechanism is the first to offer differential privacy on the joint distribution over analysts' answers, providing privacy for data an- alysts even if the other data analysts collude or register multiple accounts. In some settings, we are able to achieve nearly optimal error rates (even compared to mechanisms which do not offer an- alyst privacy), and we are able to extend our techniques to handle non-linear queries. Our analysis is based on a novel view of the private query-release problem as a two-player zero-sum game, which may be of independent interest.", acknowledgement = ack-nhfb, } @InProceedings{Nikolov:2013:GDP, author = "Aleksandar Nikolov and Kunal Talwar and Li Zhang", title = "The geometry of differential privacy: the sparse and approximate cases", crossref = "ACM:2013:SPF", pages = "351--360", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488652", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We study trade-offs between accuracy and privacy in the context of linear queries over histograms. This is a rich class of queries that includes contingency tables and range queries and has been the focus of a long line of work. For a given set of $d$ linear queries over a database $ x \in R^N $, we seek to find the differentially private mechanism that has the minimum mean squared error. For pure differential privacy, [5, 32] give an $ O(\log^2 d) $ approximation to the optimal mechanism. Our first contribution is to give an efficient $ O(\log^2 d) $ approximation guarantee for the case of $ (\epsilon, \delta) $-differential privacy. Our mechanism adds carefully chosen correlated Gaussian noise to the answers. We prove its approximation guarantee relative to the hereditary discrepancy lower bound of [44], using tools from convex geometry. We next consider the sparse case when the number of queries exceeds the number of individuals in the database, i.e. when $ d > n \Delta |x|_1 $. The lower bounds used in the previous approximation algorithm no longer apply --- in fact better mechanisms are known in this setting [7, 27, 28, 31, 49]. Our second main contribution is to give an efficient $ (\epsilon, \delta) $-differentially private mechanism that, for any given query set $A$ and an upper bound $n$ on $ |x|_1 $, has mean squared error within $ \polylog (d, N) $ of the optimal for $A$ and $n$. This approximation is achieved by coupling the Gaussian noise addition approach with linear regression over the $ l_1 $ ball. Additionally, we show a similar polylogarithmic approximation guarantee for the optimal $ \epsilon $-differentially private mechanism in this sparse setting. Our work also shows that for arbitrary counting queries, i.e. $A$ with entries in $ \{ 0, 1 \} $, there is an $ \epsilon $-differentially private mechanism with expected error $ \tilde O(\sqrt n) $ per query, improving on the $ \tilde O(n^{2 / 3}) $ bound of [7] and matching the lower bound implied by [15] up to logarithmic factors. The connection between the hereditary discrepancy and the privacy mechanism enables us to derive the first polylogarithmic approximation to the hereditary discrepancy of a matrix $A$.", acknowledgement = ack-nhfb, } @InProceedings{Ullman:2013:ACQ, author = "Jonathan Ullman", title = "Answering $ n_{2 + o(1)} $ counting queries with differential privacy is hard", crossref = "ACM:2013:SPF", pages = "361--370", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488653", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "A central problem in differentially private data analysis is how to design efficient algorithms capable of answering large numbers of counting queries on a sensitive database. Counting queries are of the form ``What fraction of individual records in the database satisfy the property $q$ ?'' We prove that if one-way functions exist, then there is no algorithm that takes as input a database $ {\rm db} \in {\rm dbset} $, and $ k = \tilde \Theta (n^2) $ arbitrary efficiently computable counting queries, runs in time $ \poly (d, n) $, and returns an approximate answer to each query, while satisfying differential privacy. We also consider the complexity of answering ``simple'' counting queries, and make some progress in this direction by showing that the above result holds even when we require that the queries are computable by constant-depth ($ {\rm AC}^0 $) circuits. Our result is almost tight because it is known that $ \tilde \Omega (n^2) $ counting queries can be answered efficiently while satisfying differential privacy. Moreover, many more than $ n^2 $ queries (even exponential in $n$) can be answered in exponential time. We prove our results by extending the connection between differentially private query release and cryptographic traitor-tracing schemes to the setting where the queries are given to the sanitizer as input, and by constructing a traitor-tracing scheme that is secure in this setting.", acknowledgement = ack-nhfb, } @InProceedings{Thorup:2013:BPS, author = "Mikkel Thorup", title = "Bottom-$k$ and priority sampling, set similarity and subset sums with minimal independence", crossref = "ACM:2013:SPF", pages = "371--380", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488655", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We consider bottom-$k$ sampling for a set X, picking a sample S$_k$ (X) consisting of the k elements that are smallest according to a given hash function h. With this sample we can estimate the relative size f=|Y|/|X| of any subset Y as |S$_k$ (X) intersect Y|/k. A standard application is the estimation of the Jaccard similarity f=|A intersect B|/|A union B| between sets A and B. Given the bottom-$k$ samples from A and B, we construct the bottom-$k$ sample of their union as S$_k$ (A union B)=S$_k$ (S$_k$ (A) union S$_k$ (B)), and then the similarity is estimated as |S$_k$ (A union B) intersect S$_k$ (A) intersect S$_k$ (B)|/k. We show here that even if the hash function is only 2-independent, the expected relative error is $ O(1 \sqrt (f_k)) $. For $ f_k = \Omega(1) $ this is within a constant factor of the expected relative error with truly random hashing. For comparison, consider the classic approach of kxmin-wise where we use $k$ hash independent functions $ h_1, \ldots {}, h_k $, storing the smallest element with each hash function. For kxmin-wise there is an at least constant bias with constant independence, and it is not reduced with larger $k$. Recently Feigenblat et al. showed that bottom-$k$ circumvents the bias if the hash function is 8-independent and $k$ is sufficiently large. We get down to 2-independence for any $k$. Our result is based on a simply union bound, transferring generic concentration bounds for the hashing scheme to the bottom-$k$ sample, e.g., getting stronger probability error bounds with higher independence. For weighted sets, we consider priority sampling which adapts efficiently to the concrete input weights, e.g., benefiting strongly from heavy-tailed input. This time, the analysis is much more involved, but again we show that generic concentration bounds can be applied.", acknowledgement = ack-nhfb, } @InProceedings{Lenzen:2013:FRT, author = "Christoph Lenzen and Boaz Patt-Shamir", title = "Fast routing table construction using small messages: extended abstract", crossref = "ACM:2013:SPF", pages = "381--390", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488656", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We describe a distributed randomized algorithm to construct routing tables. Given $ 0 < \epsilon \leq 1 / 2 $, the algorithm runs in time $ \tilde O(n^{1 / 2 + \epsilon } + {\rm HD}) $, where $n$ is the number of nodes and HD denotes the diameter of the network in hops (i.e., as if the network is unweighted). The weighted length of the produced routes is at most $ O(\epsilon^{-1} \log \epsilon^{-1}) $ times the optimal weighted length. This is the first algorithm to break the $ \Omega (n) $ complexity barrier for computing weighted shortest paths even for a single source. Moreover, the algorithm nearly meets the $ \tilde \Omega (n^{1 / 2} + {\rm HD}) $ lower bound for distributed computation of routing tables and approximate distances (with optimality, up to $ \polylog $ factors, for $ \epsilon = 1 / \log n $). The presented techniques have many applications, including improved distributed approximation algorithms for Generalized Steiner Forest, all-pairs distance estimation, and estimation of the weighted diameter.", acknowledgement = ack-nhfb, } @InProceedings{Mendes:2013:MAA, author = "Hammurabi Mendes and Maurice Herlihy", title = "Multidimensional approximate agreement in {Byzantine} asynchronous systems", crossref = "ACM:2013:SPF", pages = "391--400", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488657", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "The problem of $ \epsilon $-approximate agreement in Byzantine asynchronous systems is well-understood when all values lie on the real line. In this paper, we generalize the problem to consider values that lie in $ R^m $, for $ m \geq 1 $, and present an optimal protocol in regard to fault tolerance. Our scenario is the following. Processes start with values in $ R^m $, for $ m \geq 1 $, and communicate via message-passing. The system is asynchronous: there is no upper bound on processes' relative speeds or on message delay. Some faulty processes can display arbitrarily malicious (i.e. Byzantine) behavior. Non-faulty processes must decide on values that are: (1) in $ R^m $; (2) within distance $ \epsilon $ of each other; and (3) in the convex hull of the non-faulty processes' inputs. We give an algorithm with a matching lower bound on fault tolerance: we require $ n > t(m + 2) $, where $n$ is the number of processes, $t$ is the number of Byzantine processes, and input and output values reside in $ R^m $. Non-faulty processes send $ O(n^2 d \log (m / \epsilon \max \{ \delta (d) : 1 \leq d \leq m \})) $ messages in total, where $ \delta (d) $ is the range of non-faulty inputs projected at coordinate $d$. The Byzantine processes do not affect the algorithm's running time.", acknowledgement = ack-nhfb, } @InProceedings{King:2013:BAP, author = "Valerie King and Jared Saia", title = "{Byzantine} agreement in polynomial expected time: [extended abstract]", crossref = "ACM:2013:SPF", pages = "401--410", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488658", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "In the classic asynchronous Byzantine agreement problem, communication is via asynchronous message-passing and the adversary is adaptive with full information. In particular, the adversary can adaptively determine which processors to corrupt and what strategy these processors should use as the algorithm proceeds; the scheduling of the delivery of messages is set by the adversary, so that the delays are unpredictable to the algorithm; and the adversary knows the states of all processors at any time, and is assumed to be computationally unbounded. Such an adversary is also known as ``strong''. We present a polynomial expected time algorithm to solve asynchronous Byzantine Agreement with a strong adversary that controls up to a constant fraction of the processors. This is the first improvement in running time for this problem since Ben-Or's exponential expected time solution in 1983. Our algorithm tolerates an adversary that controls up to a $ 1 / 500 $ fraction of the processors.", acknowledgement = ack-nhfb, } @InProceedings{Chakrabarty:2013:MTB, author = "Deeparnab Chakrabarty and C. Seshadhri", title = "A $ o(n) $ monotonicity tester for {Boolean} functions over the hypercube", crossref = "ACM:2013:SPF", pages = "411--418", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488660", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Given oracle access to a Boolean function $ f : \{ 0, 1 \}^n \to \{ 0, 1 \} $, we design a randomized tester that takes as input a parameter $ \epsilon > 0 $, and outputs Yes if the function is monotonically non-increasing, and outputs No with probability $ > 2 / 3 $, if the function is $ \epsilon $-far from being monotone, that is, $f$ needs to be modified at $ \epsilon $-fraction of the points to make it monotone. Our non-adaptive, one-sided tester makes $ \tilde O(n^{5 / 6} \epsilon^{-5 / 3}) $ queries to the oracle.", acknowledgement = ack-nhfb, } @InProceedings{Chakrabarty:2013:OBM, author = "Deeparnab Chakrabarty and C. Seshadhri", title = "Optimal bounds for monotonicity and {Lipschitz} testing over hypercubes and hypergrids", crossref = "ACM:2013:SPF", pages = "419--428", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488661", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "The problem of monotonicity testing over the hypergrid and its special case, the hypercube, is a classic question in property testing. We are given query access to $ f : [k]^n \to R $ (for some ordered range $R$). The hypergrid/cube has a natural partial order given by coordinate-wise ordering, denoted by prec. A function is monotone if for all pairs $ x \prec y $, $ f(x) \leq f(y) $. The distance to monotonicity, $ \epsilon_f $, is the minimum fraction of values of $f$ that need to be changed to make f monotone. For $ k = 2 $ (the boolean hypercube), the usual tester is the edge tester, which checks monotonicity on adjacent pairs of domain points. It is known that the edge tester using $ O(\epsilon^{-1} n \log |R|) $ samples can distinguish a monotone function from one where $ \epsilon_f > \epsilon $. On the other hand, the best lower bound for monotonicity testing over general $R$ is $ \Omega (n) $. We resolve this long standing open problem and prove that $ O(n / \epsilon) $ samples suffice for the edge tester. For hypergrids, known testers require $ O(\epsilon^{-1} n \log k \log |R|) $ samples, while the best known (non-adaptive) lower bound is $ \Omega (\epsilon^{-1} n \log k) $. We give a (non-adaptive) monotonicity tester for hypergrids running in $ O(\epsilon^{{-1} n \log k}) $ time. Our techniques lead to optimal property testers (with the same running time) for the natural Lipschitz property on hypercubes and hypergrids. (A $c$-Lipschitz function is one where $ |f(x) - f(y)| \leq c || x - y ||_1 $.) In fact, we give a general unified proof for $ O(\epsilon^{-1} n \log k) $-query testers for a class of ``bounded-derivative'' properties, a class containing both monotonicity and Lipschitz.", acknowledgement = ack-nhfb, } @InProceedings{Bhattacharyya:2013:ELC, author = "Arnab Bhattacharyya and Eldar Fischer and Hamed Hatami and Pooya Hatami and Shachar Lovett", title = "Every locally characterized affine-invariant property is testable", crossref = "ACM:2013:SPF", pages = "429--436", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488662", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Set $ F = F_p $ for any fixed prime $ p \geq 2 $. An affine-invariant property is a property of functions over $ F^n $ that is closed under taking affine transformations of the domain. We prove that all affine-invariant properties having local characterizations are testable. In fact, we show a proximity-oblivious test for any such property cP, meaning that given an input function $f$, we make a constant number of queries to $f$, always accept if $f$ satisfies cP, and otherwise reject with probability larger than a positive number that depends only on the distance between $f$ and cP. More generally, we show that any affine-invariant property that is closed under taking restrictions to subspaces and has bounded complexity is testable. We also prove that any property that can be described as the property of decomposing into a known structure of low-degree polynomials is locally characterized and is, hence, testable. For example, whether a function is a product of two degree-$d$ polynomials, whether a function splits into a product of d linear polynomials, and whether a function has low rank are all examples of degree-structural properties and are therefore locally characterized. Our results depend on a new Gowers inverse theorem by Tao and Ziegler for low characteristic fields that decomposes any polynomial with large Gowers norm into a function of a small number of low-degree non-classical polynomials. We establish a new equidistribution result for high rank non-classical polynomials that drives the proofs of both the testability results and the local characterization of degree-structural properties.", acknowledgement = ack-nhfb, } @InProceedings{Kawarabayashi:2013:TSF, author = "Ken-ichi Kawarabayashi and Yuichi Yoshida", title = "Testing subdivision-freeness: property testing meets structural graph theory", crossref = "ACM:2013:SPF", pages = "437--446", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488663", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Testing a property $P$ of graphs in the bounded-degree model deals with the following problem: given a graph $G$ of bounded degree $d$, we should distinguish (with probability 2/3, say) between the case that $G$ satisfies P and the case that one should add/remove at least $ \epsilon d n $ edges of $G$ to make it satisfy $P$. In sharp contrast to property testing of dense graphs, which is relatively well understood, only few properties are known to be testable with a constant number of queries in the bounded-degree model. In particular, no global monotone (i.e., closed under edge deletions) property that expander graphs can satisfy has been shown to be testable in constant time so far. In this paper, we identify for the first time a natural family of global monotone property that expander graphs can satisfy and can be efficiently tested in the bounded degree model. Specifically, we show that, for any integer $ t \geq 1 $, $ K_t $-subdivision-freeness is testable with a constant number of queries in the bounded-degree model. This property was not previously known to be testable even with o(n) queries. Note that an expander graph with all degree less than $ t - 1 $ does not have a $ K_t $-subdivision. The proof is based on a novel combination of some results that develop the framework of partitioning oracles, together with structural graph theory results that develop the seminal graph minor theory by Robertson and Seymour. As far as we aware, this is the first result that bridges property testing and structural graph theory. Although we know a rough structure for graphs without $H$-minors from the famous graph minor theory by Robertson and Seymour, there is no corresponding structure theorem for graphs without $H$-subdivisions so far, even $ K_5 $-subdivision-free graphs. Therefore, subdivisions and minors are very different in a graph structural sense.", acknowledgement = ack-nhfb, } @InProceedings{Chan:2013:ARP, author = "Siu On Chan", title = "Approximation resistance from pairwise independent subgroups", crossref = "ACM:2013:SPF", pages = "447--456", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488665", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We show optimal (up to constant factor) NP-hardness for Max-$k$-CSP over any domain, whenever k is larger than the domain size. This follows from our main result concerning predicates over abelian groups. We show that a predicate is approximation resistant if it contains a subgroup that is balanced pairwise independent. This gives an unconditional analogue of Austrin--Mossel hardness result, bypassing the Unique-Games Conjecture for predicates with an abelian subgroup structure. Our main ingredient is a new gap-amplification technique inspired by XOR-lemmas. Using this technique, we also improve the NP-hardness of approximating Independent-Set on bounded-degree graphs, Almost-Coloring, Two-Prover-One-Round-Game, and various other problems.", acknowledgement = ack-nhfb, } @InProceedings{Huang:2013:ARS, author = "Sangxia Huang", title = "Approximation resistance on satisfiable instances for predicates with few accepting inputs", crossref = "ACM:2013:SPF", pages = "457--466", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488666", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We prove that for all integer $ k \geq 3 $, there is a predicate P on k Boolean variables with 2$^{\tilde O(k 1 / 3)}$ accepting assignments that is approximation resistant even on satisfiable instances. That is, given a satisfiable CSP instance with constraint P, we cannot achieve better approximation ratio than simply picking random assignments. This improves the best previously known result by Hastad and Khot where the predicate has 2$^{O(k 1 / 2)}$ accepting assignments. Our construction is inspired by several recent developments. One is the idea of using direct sums to improve soundness of PCPs, developed by Chan [5]. We also use techniques from Wenner [32] to construct PCPs with perfect completeness without relying on the d-to-1 Conjecture.", acknowledgement = ack-nhfb, } @InProceedings{Garg:2013:WEA, author = "Sanjam Garg and Craig Gentry and Amit Sahai and Brent Waters", title = "Witness encryption and its applications", crossref = "ACM:2013:SPF", pages = "467--476", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488667", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We put forth the concept of witness encryption. A witness encryption scheme is defined for an NP language L (with corresponding witness relation R). In such a scheme, a user can encrypt a message M to a particular problem instance x to produce a ciphertext. A recipient of a ciphertext is able to decrypt the message if x is in the language and the recipient knows a witness w where R(x,w) holds. However, if x is not in the language, then no polynomial-time attacker can distinguish between encryptions of any two equal length messages. We emphasize that the encrypter himself may have no idea whether $x$ is actually in the language. Our contributions in this paper are threefold. First, we introduce and formally define witness encryption. Second, we show how to build several cryptographic primitives from witness encryption. Finally, we give a candidate construction based on the NP-complete Exact Cover problem and Garg, Gentry, and Halevi's recent construction of ``approximate'' multilinear maps. Our method for witness encryption also yields the first candidate construction for an open problem posed by Rudich in 1989: constructing computational secret sharing schemes for an NP-complete access structure.", acknowledgement = ack-nhfb, } @InProceedings{De:2013:MSD, author = "Anindya De and Elchanan Mossel and Joe Neeman", title = "Majority is stablest: discrete and {SoS}", crossref = "ACM:2013:SPF", pages = "477--486", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488668", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "The Majority is Stablest Theorem has numerous applications in hardness of approximation and social choice theory. We give a new proof of the Majority is Stablest Theorem by induction on the dimension of the discrete cube. Unlike the previous proof, it uses neither the ``invariance principle'' nor Borell's result in Gaussian space. The new proof is general enough to include all previous variants of majority is stablest such as ``it ain't over until it's over'' and ``Majority is most predictable''. Moreover, the new proof allows us to derive a proof of Majority is Stablest in a constant level of the Sum of Squares hierarchy. This implies in particular that Khot-Vishnoi instance of Max-Cut does not provide a gap instance for the Lasserre hierarchy.", acknowledgement = ack-nhfb, } @InProceedings{Beck:2013:SEH, author = "Christopher Beck and Russell Impagliazzo", title = "Strong {ETH} holds for regular resolution", crossref = "ACM:2013:SPF", pages = "487--494", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488669", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We obtain asymptotically sharper lower bounds on resolution complexity for $k$-CNF's than was known previously. We show that for any large enough $k$ there are $k$-CNF's which require resolution width $ (1 - \tilde O(k^{-1 / 4}))n $, regular resolution size 2$^{(1 - \tilde O(k^{-1 / 4}))n}$, and general resolution size (3/2)$^{(1 - \tilde O(k - 1 / 4))n}$.", acknowledgement = ack-nhfb, } @InProceedings{Lee:2013:NCO, author = "James R. Lee and Manor Mendel and Mohammad Moharrami", title = "A node-capacitated {Okamura--Seymour} theorem", crossref = "ACM:2013:SPF", pages = "495--504", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488671", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "The classical Okamura-Seymour theorem states that for an edge-capacitated, multi-commodity flow instance in which all terminals lie on a single face of a planar graph, there exists a feasible concurrent flow if and only if the cut conditions are satisfied. Simple examples show that a similar theorem is impossible in the node-capacitated setting. Nevertheless, we prove that an approximate flow/cut theorem does hold: For some universal $ \epsilon > 0 $, if the node cut conditions are satisfied, then one can simultaneously route an $ \epsilon $-fraction of all the demands. This answers an open question of Chekuri and Kawarabayashi. More generally, we show that this holds in the setting of multi-commodity polymatroid networks introduced by Chekuri, et. al. Our approach employs a new type of random metric embedding in order to round the convex programs corresponding to these more general flow problems.", acknowledgement = ack-nhfb, } @InProceedings{Klein:2013:SRS, author = "Philip N. Klein and Shay Mozes and Christian Sommer", title = "Structured recursive separator decompositions for planar graphs in linear time", crossref = "ACM:2013:SPF", pages = "505--514", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488672", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Given a triangulated planar graph $G$ on $n$ vertices and an integer $r$ $r$-division of $G$ with few holes is a decomposition of $G$ into $ O(n / r) $ regions of size at most r such that each region contains at most a constant number of faces that are not faces of $G$ (also called holes), and such that, for each region, the total number of vertices on these faces is $ O(\sqrt r) $. We provide an algorithm for computing $r$-divisions with few holes in linear time. In fact, our algorithm computes a structure, called decomposition tree, which represents a recursive decomposition of $G$ that includes $r$-divisions for essentially all values of $r$. In particular, given an exponentially increasing sequence $ \{ \vec r \} = (r_1, r_2, \ldots {}) $, our algorithm can produce a recursive $ \{ \vec r \} $-division with few holes in linear time. $r$-divisions with few holes have been used in efficient algorithms to compute shortest paths, minimum cuts, and maximum flows. Our linear-time algorithm improves upon the decomposition algorithm used in the state-of-the-art algorithm for minimum st--cut (Italiano, Nussbaum, Sankowski, and Wulff-Nilsen, STOC 2011), removing one of the bottlenecks in the overall running time of their algorithm (analogously for minimum cut in planar and bounded-genus graphs).", acknowledgement = ack-nhfb, } @InProceedings{Roditty:2013:FAA, author = "Liam Roditty and Virginia Vassilevska Williams", title = "Fast approximation algorithms for the diameter and radius of sparse graphs", crossref = "ACM:2013:SPF", pages = "515--524", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488673", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "The diameter and the radius of a graph are fundamental topological parameters that have many important practical applications in real world networks. The fastest combinatorial algorithm for both parameters works by solving the all-pairs shortest paths problem (APSP) and has a running time of $ \tilde O(m n) $ in $m$-edge, $n$-node graphs. In a seminal paper, Aingworth, Chekuri, Indyk and Motwani [SODA'96 and SICOMP'99] presented an algorithm that computes in $ \tilde O(m \sqrt n + n^2) $ time an estimate $D$ for the diameter $D$, such that $ \lfloor 2 / 3 D \rfloor \leq^D \leq D $. Their paper spawned a long line of research on approximate APSP. For the specific problem of diameter approximation, however, no improvement has been achieved in over 15 years. Our paper presents the first improvement over the diameter approximation algorithm of Aingworth et. al, producing an algorithm with the same estimate but with an expected running time of $ \tilde O(m \sqrt n) $. We thus show that for all sparse enough graphs, the diameter can be 3/2-approximated in $ o(n^2) $ time. Our algorithm is obtained using a surprisingly simple method of neighborhood depth estimation that is strong enough to also approximate, in the same running time, the radius and more generally, all of the eccentricities, i.e. for every node the distance to its furthest node. We also provide strong evidence that our diameter approximation result may be hard to improve. We show that if for some constant $ \epsilon > 0 $ there is an $ O(m^{2 - \epsilon }) $ time $ (3 / 2 - \epsilon) $-approximation algorithm for the diameter of undirected unweighted graphs, then there is an $ O*((2 - \delta)^n) $ time algorithm for CNF-SAT on $n$ variables for constant $ \delta > 0 $, and the strong exponential time hypothesis of [Impagliazzo, Paturi, Zane JCSS'01] is false. Motivated by this negative result, we give several improved diameter approximation algorithms for special cases. We show for instance that for unweighted graphs of constant diameter $D$ not divisible by $3$, there is an $ O(m^{2 - \epsilon }) $ time algorithm that gives a $ (3 / 2 - \epsilon) $ approximation for constant $ \epsilon > 0 $. This is interesting since the diameter approximation problem is hardest to solve for small $D$.", acknowledgement = ack-nhfb, } @InProceedings{Gu:2013:PDM, author = "Albert Gu and Anupam Gupta and Amit Kumar", title = "The power of deferral: maintaining a constant-competitive {Steiner} tree online", crossref = "ACM:2013:SPF", pages = "525--534", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488674", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "In the online Steiner tree problem, a sequence of points is revealed one-by-one: when a point arrives, we only have time to add a single edge connecting this point to the previous ones, and we want to minimize the total length of edges added. Here, a tight bound has been known for two decades: the greedy algorithm maintains a tree whose cost is $ O(\log n) $ times the Steiner tree cost, and this is best possible. But suppose, in addition to the new edge we add, we have time to change a single edge from the previous set of edges: can we do much better? Can we, e.g., maintain a tree that is constant-competitive? We answer this question in the affirmative. We give a primal-dual algorithm that makes only a single swap per step (in addition to adding the edge connecting the new point to the previous ones), and such that the tree's cost is only a constant times the optimal cost. Our dual-based analysis is quite different from previous primal-only analyses. In particular, we give a correspondence between radii of dual balls and lengths of tree edges; since dual balls are associated with points and hence do not move around (in contrast to edges), we can closely monitor the edge lengths based on the dual radii. Showing that these dual radii cannot change too rapidly is the technical heart of the paper, and allows us to give a hard bound on the number of swaps per arrival, while maintaining a constant-competitive tree at all times. Previous results for this problem gave an algorithm that performed an amortized constant number of swaps: for each n, the number of swaps in the first $n$ steps was O(n). We also give a simpler tight analysis for this amortized case.", acknowledgement = ack-nhfb, } @InProceedings{Buchbinder:2013:SPE, author = "Niv Buchbinder and Joseph (Seffi) Naor and Roy Schwartz", title = "Simplex partitioning via exponential clocks and the multiway cut problem", crossref = "ACM:2013:SPF", pages = "535--544", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488675", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "The Multiway-Cut problem is a fundamental graph partitioning problem in which the objective is to find a minimum weight set of edges disconnecting a given set of special vertices called terminals. This problem is NP-hard and there is a well known geometric relaxation in which the graph is embedded into a high dimensional simplex. Rounding a solution to the geometric relaxation is equivalent to partitioning the simplex. We present a novel simplex partitioning algorithm which is based on em competing exponential clocks and distortion. Unlike previous methods, it utilizes cuts that are not parallel to the faces of the simplex. Applying this partitioning algorithm to the multiway cut problem, we obtain a simple (4/3)-approximation algorithm, thus, improving upon the current best known result. This bound is further pushed to obtain an approximation factor of 1.32388. It is known that under the assumption of the unique games conjecture, the best possible approximation for the Multiway-Cut problem can be attained via the geometric relaxation.", acknowledgement = ack-nhfb, } @InProceedings{Gorbunov:2013:ABE, author = "Sergey Gorbunov and Vinod Vaikuntanathan and Hoeteck Wee", title = "Attribute-based encryption for circuits", crossref = "ACM:2013:SPF", pages = "545--554", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488677", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "In an attribute-based encryption (ABE) scheme, a ciphertext is associated with an $l$-bit public index pind and a message $m$, and a secret key is associated with a Boolean predicate $P$. The secret key allows to decrypt the ciphertext and learn $m$ iff $P({\rm pind}) = 1$. Moreover, the scheme should be secure against collusions of users, namely, given secret keys for polynomially many predicates, an adversary learns nothing about the message if none of the secret keys can individually decrypt the ciphertext. We present attribute-based encryption schemes for circuits of any arbitrary polynomial size, where the public parameters and the ciphertext grow linearly with the depth of the circuit. Our construction is secure under the standard learning with errors (LWE) assumption. Previous constructions of attribute-based encryption were for Boolean formulas, captured by the complexity class ${\rm NC}^1 $. In the course of our construction, we present a new framework for constructing ABE schemes. As a by-product of our framework, we obtain ABE schemes for polynomial-size branching programs, corresponding to the complexity class LOGSPACE, under quantitatively better assumptions.", acknowledgement = ack-nhfb, } @InProceedings{Goldwasser:2013:RGC, author = "Shafi Goldwasser and Yael Kalai and Raluca Ada Popa and Vinod Vaikuntanathan and Nickolai Zeldovich", title = "Reusable garbled circuits and succinct functional encryption", crossref = "ACM:2013:SPF", pages = "555--564", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488678", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Garbled circuits, introduced by Yao in the mid 80s, allow computing a function f on an input x without leaking anything about f or x besides f(x). Garbled circuits found numerous applications, but every known construction suffers from one limitation: it offers no security if used on multiple inputs x. In this paper, we construct for the first time reusable garbled circuits. The key building block is a new succinct single-key functional encryption scheme. Functional encryption is an ambitious primitive: given an encryption $ {\rm Enc}(x) $ of a value $x$, and a secret key $ {\rm sk}_f $ for a function $f$, anyone can compute $ f(x) $ without learning any other information about $x$. We construct, for the first time, a succinct functional encryption scheme for {\em any} polynomial-time function f where succinctness means that the ciphertext size does not grow with the size of the circuit for $f$, but only with its depth. The security of our construction is based on the intractability of the Learning with Errors (LWE) problem and holds as long as an adversary has access to a single key $ {\rm sk}_f $ (or even an a priori bounded number of keys for different functions). Building on our succinct single-key functional encryption scheme, we show several new applications in addition to reusable garbled circuits, such as a paradigm for general function obfuscation which we call token-based obfuscation, homomorphic encryption for a class of Turing machines where the evaluation runs in input-specific time rather than worst-case time, and a scheme for delegating computation which is publicly verifiable and maintains the privacy of the computation.", acknowledgement = ack-nhfb, } @InProceedings{Kalai:2013:DBS, author = "Yael Tauman Kalai and Ran Raz and Ron D. Rothblum", title = "Delegation for bounded space", crossref = "ACM:2013:SPF", pages = "565--574", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488679", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We construct a 1-round delegation scheme for every language computable in time t=t(n) and space s=s(n), where the running time of the prover is poly(t) and the running time of the verifier is $ \tilde O(n + p o l y(s)) $ (where $ \tilde O $ hides $ \polylog (t) $ factors). The proof exploits a curious connection between the problem of computation delegation and the model of multi-prover interactive proofs that are sound against no-signaling (cheating) strategies, a model that was studied in the context of multi-prover interactive proofs with provers that share quantum entanglement, and is motivated by the physical principle that information cannot travel faster than light. For any language computable in time $ t = t(n) $ and space $ s = s(n) $, we construct MIPs that are sound against no-signaling strategies, where the running time of the provers is $ \poly (t) $, the number of provers is $ \tilde O(s) $, and the running time of the verifier is $ \tilde O(s + n) $. We then show how to use the method suggested by Aiello et-al (ICALP, 2000) to convert our MIP into a 1-round delegation scheme, by using a computational private information retrieval (PIR) scheme. Thus, assuming the existence of a sub-exponentially secure PIR scheme, we get our 1-round delegation scheme.", acknowledgement = ack-nhfb, } @InProceedings{Brakerski:2013:CHL, author = "Zvika Brakerski and Adeline Langlois and Chris Peikert and Oded Regev and Damien Stehl{\'e}", title = "Classical hardness of learning with errors", crossref = "ACM:2013:SPF", pages = "575--584", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488680", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We show that the Learning with Errors (LWE) problem is classically at least as hard as standard worst-case lattice problems. Previously this was only known under quantum reductions. Our techniques capture the tradeoff between the dimension and the modulus of LWE instances, leading to a much better understanding of the landscape of the problem. The proof is inspired by techniques from several recent cryptographic constructions, most notably fully homomorphic encryption schemes.", acknowledgement = ack-nhfb, } @InProceedings{Ben-Sasson:2013:CEP, author = "Eli Ben-Sasson and Alessandro Chiesa and Daniel Genkin and Eran Tromer", title = "On the concrete efficiency of probabilistically-checkable proofs", crossref = "ACM:2013:SPF", pages = "585--594", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488681", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Probabilistically-Checkable Proofs (PCPs) form the algorithmic core that enables fast verification of long computations in many cryptographic constructions. Yet, despite the wonderful asymptotic savings they bring, PCPs are also the infamous computational bottleneck preventing these powerful cryptographic constructions from being used in practice. To address this problem, we present several results about the computational efficiency of PCPs. We construct the first PCP where the prover and verifier time complexities are quasi-optimal (i.e., optimal up to poly-logarithmic factors). The prover and verifier are also highly-parallelizable, and these computational guarantees hold even when proving and verifying the correctness of random-access machine computations. Our construction is explicit and has the requisite properties for being used in the cryptographic applications mentioned above. Next, to better understand the efficiency of our PCP, we propose a new efficiency measure for PCPs (and their major components, locally-testable codes and PCPs of proximity). We define a concrete-efficiency threshold that indicates the smallest problem size beyond which the PCP becomes ``useful'', in the sense that using it is cheaper than performing naive verification (i.e., rerunning the computation); our definition accounts for both the prover and verifier complexity. We then show that our PCP has a finite concrete-efficiency threshold. That such a PCP exists does not follow from existing works on PCPs with polylogarithmic-time verifiers. As in [Ben-Sasson and Sudan, STOC '05], PCPs of proximity for Reed--Solomon (RS) codes are the main component of our PCP. We construct a PCP of proximity that reduces the concrete-efficiency threshold for testing proximity to RS codes from 2$^{683}$ in their work to 2$^{43}$, which is tantalizingly close to practicality.", acknowledgement = ack-nhfb, } @InProceedings{Cadek:2013:ECM, author = "Martin Cadek and Marek Krcal and Jiri Matousek and Lukas Vokrinek and Uli Wagner", title = "Extending continuous maps: polynomiality and undecidability", crossref = "ACM:2013:SPF", pages = "595--604", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488683", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We consider several basic problems of algebraic topology, with connections to combinatorial and geometric questions, from the point of view of computational complexity. The extension problem asks, given topological spaces $X$, $Y$, a subspace $ A \subseteq X $, and a (continuous) map $ f : A \to Y $, whether $f$ can be extended to a map $ X \to Y $. For computational purposes, we assume that X and Y are represented as finite simplicial complexes, $A$ is a subcomplex of $X$, and $f$ is given as a simplicial map. In this generality the problem is undecidable, as follows from Novikov's result from the 1950s on uncomputability of the fundamental group $ \pi_1 (Y) $. We thus study the problem under the assumption that, for some $ k \geq 2 $, $Y$ is $ (k - 1) $-connected; informally, this means that $Y$ has ``no holes up to dimension $ k - 1 $'' i.e., the first $ k - 1 $ homotopy groups of $Y$ vanish (a basic example of such a $Y$ is the sphere $ S^k $). We prove that, on the one hand, this problem is still undecidable for $ \dim X = 2 k $. On the other hand, for every fixed $ k \geq 2 $, we obtain an algorithm that solves the extension problem in polynomial time assuming $Y$ $ (k - 1) $-connected and $ \dim X \leq 2 k - 1 $. For $ \dim X \leq 2 k - 2 $, the algorithm also provides a classification of all extensions up to homotopy (continuous deformation). This relies on results of our SODA 2012 paper, and the main new ingredient is a machinery of objects with polynomial-time homology, which is a polynomial-time analog of objects with effective homology developed earlier by Sergeraert et al. We also consider the computation of the higher homotopy groups $ \pi_k (Y) $, $ k \geq 2 $, for a 1-connected $Y$. Their computability was established by Brown in 1957; we show that $ \pi_k(Y) $ can be computed in polynomial time for every fixed $ k \geq 2 $. On the other hand, Anick proved in 1989 that computing $ \pi_k(Y) $ is \#P-hard if $k$ is a part of input, where $Y$ is a cell complex with certain rather compact encoding. We strengthen his result to \#P-hardness for $Y$ given as a simplicial complex.", acknowledgement = ack-nhfb, } @InProceedings{Har-Peled:2013:NPL, author = "Sariel Har-Peled and Benjamin Adam Raichel", title = "Net and prune: a linear time algorithm for {Euclidean} distance problems", crossref = "ACM:2013:SPF", pages = "605--614", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488684", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We provide a general framework for getting linear time constant factor approximations (and in many cases FPTAS's) to a copious amount of well known and well studied problems in Computational Geometry, such as $k$-center clustering and furthest nearest neighbor. The new approach is robust to variations in the input problem, and yet it is simple, elegant and practical. In particular, many of these well studied problems which fit easily into our framework, either previously had no linear time approximation algorithm, or required rather involved algorithms and analysis. A short list of the problems we consider include furthest nearest neighbor, $k$-center clustering, smallest disk enclosing k points, $k$-th largest distance, $k$-th smallest $m$-nearest neighbor distance, $k$-th heaviest edge in the MST and other spanning forest type problems, problems involving upward closed set systems, and more. Finally, we show how to extend our framework such that the linear running time bound holds with high probability.", acknowledgement = ack-nhfb, } @InProceedings{Caputo:2013:RLT, author = "Pietro Caputo and Fabio Martinelli and Alistair Sinclair and Alexandre Stauffer", title = "Random lattice triangulations: structure and algorithms", crossref = "ACM:2013:SPF", pages = "615--624", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488685", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "The paper concerns lattice triangulations, i.e., triangulations of the integer points in a polygon in $ R^2 $ whose vertices are also integer points. Lattice triangulations have been studied extensively both as geometric objects in their own right and by virtue of applications in algebraic geometry. Our focus is on random triangulations in which a triangulation $ \sigma $ has weight $ \lambda^{| \sigma |} $, where $ \lambda $ is a positive real parameter and $ | \sigma | $ is the total length of the edges in $ \sigma $. Empirically, this model exhibits a ``phase transition'' at $ \lambda = 1 $ (corresponding to the uniform distribution): for $ \lambda < 1 $ distant edges behave essentially independently, while for $ \lambda > 1 $ very large regions of aligned edges appear. We substantiate this picture as follows. For $ \lambda < 1 $ sufficiently small, we show that correlations between edges decay exponentially with distance (suitably defined), and also that the Glauber dynamics (a local Markov chain based on flipping edges) is rapidly mixing (in time polynomial in the number of edges). This dynamics has been proposed by several authors as an algorithm for generating random triangulations. By contrast, for $ \lambda > 1 $ we show that the mixing time is exponential. These are apparently the first rigorous quantitative results on spatial mixing properties and dynamics of random lattice triangulations.", acknowledgement = ack-nhfb, } @InProceedings{Sinclair:2013:LYT, author = "Alistair Sinclair and Piyush Srivastava", title = "{Lee--Yang} theorems and the complexity of computing averages", crossref = "ACM:2013:SPF", pages = "625--634", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488686", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We study the complexity of computing average quantities related to spin systems, such as the mean magnetization and susceptibility in the ferromagnetic Ising model, and the average dimer count (or average size of a matching) in the monomer-dimer model. By establishing connections between the complexity of computing these averages and the location of the complex zeros of the partition function, we show that these averages are \#P-hard to compute. In case of the Ising model, our approach requires us to prove an extension of the famous Lee--Yang Theorem from the 1950s.", acknowledgement = ack-nhfb, } @InProceedings{Cai:2013:CDR, author = "Jin-Yi Cai and Heng Guo and Tyson Williams", title = "A complete dichotomy rises from the capture of vanishing signatures: extended abstract", crossref = "ACM:2013:SPF", pages = "635--644", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488687", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We prove a complexity dichotomy theorem for Holant problems over an arbitrary set of complex-valued symmetric constraint functions {F} on Boolean variables. This extends and unifies all previous dichotomies for Holant problems on symmetric constraint functions (taking values without a finite modulus). We define and characterize all symmetric vanishing signatures. They turned out to be essential to the complete classification of Holant problems. The dichotomy theorem has an explicit tractability criterion. A Holant problem defined by a set of constraint functions {F} is solvable in polynomial time if it satisfies this tractability criterion, and is \#P-hard otherwise. The tractability criterion can be intuitively stated as follows: A set {F} is tractable if (1) every function in {F} has arity at most two, or (2) {F} is transformable to an affine type, or (3) {F} is transformable to a product type, or (4) {F} is vanishing, combined with the right type of binary functions, or (5) {F} belongs to a special category of vanishing type Fibonacci gates. The proof of this theorem utilizes many previous dichotomy theorems on Holant problems and Boolean \#CSP. Holographic transformations play an indispensable role, not only as a proof technique, but also in the statement of the dichotomy criterion.", acknowledgement = ack-nhfb, } @InProceedings{Miller:2013:SLO, author = "Gary L. Miller", title = "Solving large optimization problems using spectral graph theory", crossref = "ACM:2013:SPF", pages = "981--981", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488689", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Spectral Graph Theory is the interplay between linear algebra and combinatorial graph theory. One application of this interplay is a nearly linear time solver for Symmetric Diagonally Dominate systems (SDD). This seemingly restrictive class of systems has received much interest in the last 15 years. Both algorithm design theory and practical implementations have made substantial progress. There is also a growing number of problems that can be efficiently solved using SDD solvers including: image segmentation, image denoising, finding solutions to elliptic equations, computing maximum flow in a graph, graph sparsification, and graphics. All these examples can be viewed as special case of convex optimization problems.", acknowledgement = ack-nhfb, } @InProceedings{Elkin:2013:OES, author = "Michael Elkin and Shay Solomon", title = "Optimal {Euclidean} spanners: really short, thin and lanky", crossref = "ACM:2013:SPF", pages = "645--654", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488691", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "The degree, the (hop-)diameter, and the weight are the most basic and well-studied parameters of geometric spanners. In a seminal STOC'95 paper, titled ``Euclidean spanners: short, thin and lanky'', Arya et al. [2] devised a construction of Euclidean $ (1 + \epsilon) $-spanners that achieves constant degree, diameter $ O(\log n) $, weight $ O(\log^2 n) \cdot \omega ({\rm MST}) $, and has running time $ O(n \cdot \log n) $. This construction applies to $n$-point constant-dimensional Euclidean spaces. Moreover, Arya et al. conjectured that the weight bound can be improved by a logarithmic factor, without increasing the degree and the diameter of the spanner, and within the same running time. This conjecture of Arya et al. became one of the most central open problems in the area of Euclidean spanners. Nevertheless, the only progress since 1995 towards its resolution was achieved in the lower bounds front: Any spanner with diameter $ O(\log n) $ must incur weight $ \Omega (\log n) \cdot \omega ({\rm MST}) $, and this lower bound holds regardless of the stretch or the degree of the spanner [12, 1]. In this paper we resolve the long-standing conjecture of Arya et al. in the affirmative. We present a spanner construction with the same stretch, degree, diameter, and running time, as in Arya et al.'s result, but with optimal weight $ O(\log n) \cdot \omega ({\rm MST}) $. So our spanners are as thin and lanky as those of Arya et al., but they are really short! Moreover, our result is more general in three ways. First, we demonstrate that the conjecture holds true not only in constant-dimensional Euclidean spaces, but also in doubling metrics. Second, we provide a general tradeoff between the three involved parameters, which is tight in the entire range. Third, we devise a transformation that decreases the lightness of spanners in general metrics, while keeping all their other parameters in check. Our main result is obtained as a corollary of this transformation.", acknowledgement = ack-nhfb, } @InProceedings{Feldman:2013:SAL, author = "Vitaly Feldman and Elena Grigorescu and Lev Reyzin and Santosh Vempala and Ying Xiao", title = "Statistical algorithms and a lower bound for detecting planted cliques", crossref = "ACM:2013:SPF", pages = "655--664", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488692", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We introduce a framework for proving lower bounds on computational problems over distributions, based on a class of algorithms called statistical algorithms. For such algorithms, access to the input distribution is limited to obtaining an estimate of the expectation of any given function on a sample drawn randomly from the input distribution, rather than directly accessing samples. Most natural algorithms of interest in theory and in practice, e.g., moments-based methods, local search, standard iterative methods for convex optimization, MCMC and simulated annealing, are statistical algorithms or have statistical counterparts. Our framework is inspired by and generalize the statistical query model in learning theory [34]. Our main application is a nearly optimal lower bound on the complexity of any statistical algorithm for detecting planted bipartite clique distributions (or planted dense subgraph distributions) when the planted clique has size $ O(n^{1 / 2 - \delta}) $ for any constant $ \delta > 0 $. Variants of these problems have been assumed to be hard to prove hardness for other problems and for cryptographic applications. Our lower bounds provide concrete evidence of hardness, thus supporting these assumptions.", acknowledgement = ack-nhfb, } @InProceedings{Jain:2013:LRM, author = "Prateek Jain and Praneeth Netrapalli and Sujay Sanghavi", title = "Low-rank matrix completion using alternating minimization", crossref = "ACM:2013:SPF", pages = "665--674", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488693", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Alternating minimization represents a widely applicable and empirically successful approach for finding low-rank matrices that best fit the given data. For example, for the problem of low-rank matrix completion, this method is believed to be one of the most accurate and efficient, and formed a major component of the winning entry in the Netflix Challenge [17]. In the alternating minimization approach, the low-rank target matrix is written in a bi-linear form, i.e. X = UV$^+$; the algorithm then alternates between finding the best U and the best V. Typically, each alternating step in isolation is convex and tractable. However the overall problem becomes non-convex and is prone to local minima. In fact, there has been almost no theoretical understanding of when this approach yields a good result. In this paper we present one of the first theoretical analyses of the performance of alternating minimization for matrix completion, and the related problem of matrix sensing. For both these problems, celebrated recent results have shown that they become well-posed and tractable once certain (now standard) conditions are imposed on the problem. We show that alternating minimization also succeeds under similar conditions. Moreover, compared to existing results, our paper shows that alternating minimization guarantees faster (in particular, geometric) convergence to the true matrix, while allowing a significantly simpler analysis.", acknowledgement = ack-nhfb, } @InProceedings{Alon:2013:ARM, author = "Noga Alon and Troy Lee and Adi Shraibman and Santosh Vempala", title = "The approximate rank of a matrix and its algorithmic applications: approximate rank", crossref = "ACM:2013:SPF", pages = "675--684", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488694", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We study the $ \epsilon $-rank of a real matrix A, defined for any $ \epsilon > 0 $ as the minimum rank over matrices that approximate every entry of $A$ to within an additive $ \epsilon $. This parameter is connected to other notions of approximate rank and is motivated by problems from various topics including communication complexity, combinatorial optimization, game theory, computational geometry and learning theory. Here we give bounds on the $ \epsilon $-rank and use them for algorithmic applications. Our main algorithmic results are (a) polynomial-time additive approximation schemes for Nash equilibria for 2-player games when the payoff matrices are positive semidefinite or have logarithmic rank and (b) an additive PTAS for the densest subgraph problem for similar classes of weighted graphs. We use combinatorial, geometric and spectral techniques; our main new tool is an algorithm for efficiently covering a convex body with translates of another convex body.", acknowledgement = ack-nhfb, } @InProceedings{Harris:2013:CSP, author = "David G. Harris and Aravind Srinivasan", title = "Constraint satisfaction, packet routing, and the {Lovasz} local lemma", crossref = "ACM:2013:SPF", pages = "685--694", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488696", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Constraint-satisfaction problems (CSPs) form a basic family of NP-hard optimization problems that includes satisfiability. Motivated by the sufficient condition for the satisfiability of SAT formulae that is offered by the Lovasz Local Lemma, we seek such sufficient conditions for arbitrary CSPs. To this end, we identify a variable-covering radius--type parameter for the infeasible configurations of a given CSP, and also develop an extension of the Lovasz Local Lemma in which many of the events to be avoided have probabilities arbitrarily close to one; these lead to a general sufficient condition for the satisfiability of arbitrary CSPs. One primary application is to packet-routing in the classical Leighton-Maggs-Rao setting, where we introduce several additional ideas in order to prove the existence of near-optimal schedules; further applications in combinatorial optimization are also shown.", acknowledgement = ack-nhfb, } @InProceedings{Thapper:2013:CFV, author = "Johan Thapper and Stanislav Zivny", title = "The complexity of finite-valued {CSPs}", crossref = "ACM:2013:SPF", pages = "695--704", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488697", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Let $ \Gamma $ be a set of rational-valued functions on a fixed finite domain; such a set is called a finite-valued constraint language. The valued constraint satisfaction problem, VCSP( $ \Gamma $), is the problem of minimising a function given as a sum of functions from $ \Gamma $ . We establish a dichotomy theorem with respect to exact solvability for all finite-valued languages defined on domains of arbitrary finite size. We show that every core language $ \Gamma $ either admits a binary idempotent and symmetric fractional polymorphism in which case the basic linear programming relaxation solves any instance of VCSP( $ \Gamma $) exactly, or $ \Gamma $ satisfies a simple hardness condition that allows for a polynomial-time reduction from Max-Cut to VCSP( $ \Gamma $). In other words, there is a single algorithm for all tractable cases and a single reason for intractability. Our results show that for exact solvability of VCSPs the basic linear programming relaxation suffices and semidefinite relaxations do not add any power. Our results generalise all previous partial classifications of finite-valued languages: the classification of {0,1}-valued languages containing all unary functions obtained by Deineko et al. [JACM'06]; the classifications of {0,1}-valued languages on two-element, three-element, and four-element domains obtained by Creignou [JCSS'95], Jonsson et al. [SICOMP'06], and Jonsson et al.[CP'11], respectively; the classifications of finite-valued languages on two-element and three-element domains obtained by Cohen et al. [AIJ'06] and Huber et al. [SODA'13], respectively; the classification of finite-valued languages containing all {0,1}-valued unary functions obtained by Kolmogorov and Zivny [JACM'13]; and the classification of Min-0-Ext problems obtained by Hirai [SODA'13].", acknowledgement = ack-nhfb, } @InProceedings{Coja-Oghlan:2013:GAK, author = "Amin Coja-Oghlan and Konstantinos Panagiotou", title = "Going after the {k-SAT} threshold", crossref = "ACM:2013:SPF", pages = "705--714", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488698", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Random $k$-SAT is the single most intensely studied example of a random constraint satisfaction problem. But despite substantial progress over the past decade, the threshold for the existence of satisfying assignments is not known precisely for any $ k \geq 3 $. The best current results, based on the second moment method, yield upper and lower bounds that differ by an additive $ k \cdot {\ln 2} / 2 $, a term that is unbounded in $k$ (Achlioptas, Peres: STOC 2003). The basic reason for this gap is the inherent asymmetry of the Boolean values 'true' and 'false' in contrast to the perfect symmetry, e.g., among the various colors in a graph coloring problem. Here we develop a new asymmetric second moment method that allows us to tackle this issue head on for the first time in the theory of random CSPs. This technique enables us to compute the $k$-SAT threshold up to an additive $ \ln 2 - 1 / 2 + O(1 / k) \sim 0.19 $. Independently of the rigorous work, physicists have developed a sophisticated but non-rigorous technique called the ``cavity method'' for the study of random CSPs (Mezard, Parisi, Zecchina: Science~2002). Our result matches the best bound that can be obtained from the so-called ``replica symmetric'' version of the cavity method, and indeed our proof directly harnesses parts of the physics calculations.", acknowledgement = ack-nhfb, } @InProceedings{Kol:2013:ICC, author = "Gillat Kol and Ran Raz", title = "Interactive channel capacity", crossref = "ACM:2013:SPF", pages = "715--724", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488699", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We study the interactive channel capacity of an $ \epsilon $-noisy channel. The interactive channel capacity $ C(\epsilon) $ is defined as the minimal ratio between the communication complexity of a problem (over a non-noisy channel), and the communication complexity of the same problem over the binary symmetric channel with noise rate $ \epsilon $, where the communication complexity tends to infinity. Our main result is the upper bound $ C(\epsilon) \leq 1 - \Omega (\sqrt H(\epsilon)) $. This compares with Shannon's non-interactive channel capacity of $ 1 - H(\epsilon) $. In particular, for a small enough $ \epsilon $, our result gives the first separation between interactive and non-interactive channel capacity, answering an open problem by Schulman [Schulman1]. We complement this result by the lower bound $ C(\epsilon) \geq 1 - O(\sqrt H(\epsilon)) $, proved for the case where the players take alternating turns.", acknowledgement = ack-nhfb, } @InProceedings{Bernstein:2013:MSP, author = "Aaron Bernstein", title = "Maintaining shortest paths under deletions in weighted directed graphs: [extended abstract]", crossref = "ACM:2013:SPF", pages = "725--734", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488701", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We present an improved algorithm for maintaining all-pairs $ 1 + \epsilon $ approximate shortest paths under deletions and weight-increases. The previous state of the art for this problem was total update time $ \tilde O (n^2 \sqrt m / \epsilon) $ for directed, unweighted graphs [2], and $ \tilde O(m n / \epsilon) $ for undirected, unweighted graphs [12]. Both algorithms were randomized and had constant query time. Note that $ \tilde O(m n) $ is a natural barrier because even with a $ (1 + \epsilon) $ approximation, there is no $ o(m n) $ combinatorial algorithm for the static all-pairs shortest path problem. Our algorithm works on directed, weighted graphs and has total (randomized) update time $ \tilde O (m n \log (R) / \epsilon) $ where $R$ is the ratio of the largest edge weight ever seen in the graph, to the smallest such weight (our query time is constant). Note that $ \log (R) = O(\log (n)) $ as long as weights are polynomial in $n$. Although $ \tilde O(m n \log (R) / \epsilon) $ is the total time over all updates, our algorithm also requires a clearly unavoidable constant time per update. Thus, we effectively expand the $ \tilde O(m n) $ total update time bound from undirected, unweighted graphs to directed graphs with polynomial weights. This is in fact the first non-trivial algorithm for decremental all-pairs shortest paths that works on weighted graphs (previous algorithms could only handle small integer weights). By a well known reduction from decremental algorithms to fully dynamic ones [9], our improved decremental algorithm leads to improved query-update tradeoffs for fully dynamic $ (1 + \epsilon) $ approximate APSP algorithm in directed graphs.", acknowledgement = ack-nhfb, } @InProceedings{Eisenstat:2013:LTA, author = "David Eisenstat and Philip N. Klein", title = "Linear-time algorithms for max flow and multiple-source shortest paths in unit-weight planar graphs", crossref = "ACM:2013:SPF", pages = "735--744", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488702", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We give simple linear-time algorithms for two problems in planar graphs: max st-flow in directed graphs with unit capacities, and multiple-source shortest paths in undirected graphs with unit lengths.", acknowledgement = ack-nhfb, } @InProceedings{Neiman:2013:SDA, author = "Ofer Neiman and Shay Solomon", title = "Simple deterministic algorithms for fully dynamic maximal matching", crossref = "ACM:2013:SPF", pages = "745--754", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488703", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "A maximal matching can be maintained in fully dynamic (supporting both addition and deletion of edges) $n$-vertex graphs using a trivial deterministic algorithm with a worst-case update time of $ O(n) $. No deterministic algorithm that outperforms the naive $ O(n) $ one was reported up to this date. The only progress in this direction is due to Ivkovic and Lloyd [14], who in 1993 devised a deterministic algorithm with an amortized update time of O((n+m)$^{ \sqrt 2 / 2}$), where m is the number of edges. In this paper we show the first deterministic fully dynamic algorithm that outperforms the trivial one. Specifically, we provide a deterministic worst-case update time of $ O(\sqrt m) $. Moreover, our algorithm maintains a matching which is in fact a 3/2-approximate maximum cardinality matching (MCM). We remark that no fully dynamic algorithm for maintaining $ (2 - \epsilon) $-approximate MCM improving upon the naive $ O(n) $ was known prior to this work, even allowing amortized time bounds and randomization. For low arboricity graphs (e.g., planar graphs and graphs excluding fixed minors), we devise another simple deterministic algorithm with sub-logarithmic update time. Specifically, it maintains a fully dynamic maximal matching with amortized update time of $ O(\log n / \log \log n) $. This result addresses an open question of Onak and Rubinfeld [19]. We also show a deterministic algorithm with optimal space usage of $ O(n + m) $, that for arbitrary graphs maintains a maximal matching with amortized update time of $ O(\sqrt m) $.", acknowledgement = ack-nhfb, } @InProceedings{Lee:2013:NAC, author = "Yin Tat Lee and Satish Rao and Nikhil Srivastava", title = "A new approach to computing maximum flows using electrical flows", crossref = "ACM:2013:SPF", pages = "755--764", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488704", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We give an algorithm which computes a $ (1 - \epsilon) $-approximately maximum st-flow in an undirected uncapacitated graph in time $ O(1 / \epsilon \sqrt m / F \cdot m \log^2 n) $ where $F$ is the flow value. By trading this off against the Karger-Levine algorithm for undirected graphs which takes $ \tilde O(m + n F) $ time, we obtain a running time of $ \tilde O(m n^{1 / 3} / \epsilon^{2 / 3}) $ for uncapacitated graphs, improving the previous best dependence on $ \epsilon $ by a factor of $ O(1 / \epsilon^3) $. Like the algorithm of Christiano, Kelner, Madry, Spielman and Teng, our algorithm reduces the problem to electrical flow computations which are carried out in linear time using fast Laplacian solvers. However, in contrast to previous work, our algorithm does not reweight the edges of the graph in any way, and instead uses local (i.e., non s-t) electrical flows to reroute the flow on congested edges. The algorithm is simple and may be viewed as trying to find a point at the intersection of two convex sets (the affine subspace of st-flows of value $F$ and the $ l_\infty $ ball) by an accelerated version of the method of alternating projections due to Nesterov. By combining this with Ford and Fulkerson's augmenting paths algorithm, we obtain an exact algorithm with running time $ \tilde O(m^{5 / 4} F^{1 / 4}) $ for uncapacitated undirected graphs, improving the previous best running time of $ \tilde O(m + \min (n F, m^{3 / 2})) $. We give a related algorithm with the same running time for approximate minimum cut, based on minimizing a smoothed version of the $ l_1 $ norm inside the cut space of the input graph. We show that the minimizer of this norm is related to an approximate blocking flow and use this to give an algorithm for computing a length $k$ approximately blocking flow in time $ \tilde O(m \sqrt k) $.", acknowledgement = ack-nhfb, } @InProceedings{Orlin:2013:MFN, author = "James B. Orlin", title = "{Max} flows in {$ O(n m) $} time, or better", crossref = "ACM:2013:SPF", pages = "765--774", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488705", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "In this paper, we present improved polynomial time algorithms for the max flow problem defined on sparse networks with $n$ nodes and $m$ arcs. We show how to solve the max flow problem in $ O(n m + m^{31 / 16} \log^2 n) $ time. In the case that $ m = O(n^{1.06}) $, this improves upon the best previous algorithm due to King, Rao, and Tarjan, who solved the max flow problem in $ O(n m \log_{m / (n \log n)} n) $ time. This establishes that the max flow problem is solvable in $ O(n m) $ time for all values of $n$ and $m$. In the case that $ m = O(n) $, we improve the running time to $ O(n^2 / \log n) $.", acknowledgement = ack-nhfb, } @InProceedings{Bringmann:2013:SSD, author = "Karl Bringmann and Kasper Green Larsen", title = "Succinct sampling from discrete distributions", crossref = "ACM:2013:SPF", pages = "775--782", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488707", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We revisit the classic problem of sampling from a discrete distribution: Given n non-negative w-bit integers x$_1$ ,..,x$_n$, the task is to build a data structure that allows sampling i with probability proportional to x$_i$. The classic solution is Walker's alias method that takes, when implemented on a Word RAM, $ O(n) $ preprocessing time, $ O(1) $ expected query time for one sample, and $ n(w + 2 \lg (n) + o(1)) $ bits of space. Using the terminology of succinct data structures, this solution has redundancy $ 2 n \lg (n) + o(n) $ bits, i.e., it uses $ 2 n \lg (n) + o(n) $ bits in addition to the information theoretic minimum required for storing the input. In this paper, we study whether this space usage can be improved. In the systematic case, in which the input is read-only, we present a novel data structure using $ r + O(w) $ redundant bits, $ O(n / r) $ expected query time and $ O(n) $ preprocessing time for any $r$. This is an improvement in redundancy by a factor of $ \Omega (\log n) $ over the alias method for $ r = n $, even though the alias method is not systematic. Moreover, we complement our data structure with a lower bound showing that this trade-off is tight for systematic data structures. In the non-systematic case, in which the input numbers may be represented in more clever ways than just storing them one-by-one, we demonstrate a very surprising separation from the systematic case: With only 1 redundant bit, it is possible to support optimal $ O(1) $ expected query time and $ O(n) $ preprocessing time! On the one hand, our results improve upon the space requirement of the classic solution for a fundamental sampling problem, on the other hand, they provide the strongest known separation between the systematic and non-systematic case for any data structure problem. Finally, we also believe our upper bounds are practically efficient and simpler than Walker's alias method.", acknowledgement = ack-nhfb, } @InProceedings{Li:2013:NIS, author = "Xin Li", title = "New independent source extractors with exponential improvement", crossref = "ACM:2013:SPF", pages = "783--792", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488708", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We study the problem of constructing explicit extractors for independent general weak random sources. For weak sources on $n$ bits with min-entropy $k$, previously the best known extractor needs to use at least $ \log n / \log k $ independent sources [22, 3]. In this paper we give a new extractor that only uses $ O(\log (\log n / \log k)) + O(1) $ independent sources. Thus, our result improves the previous best result exponentially. We then use our new extractor to give improved network extractor protocols, as defined in [14]. The network extractor protocols also give new results in distributed computing with general weak random sources, which dramatically improve previous results. For example, we can tolerate a nearly optimal fraction of faulty players in synchronous Byzantine agreement and leader election, even if the players only have access to independent $n$-bit weak random sources with min-entropy as small as $ k = \polylog (n) $. Our extractor for independent sources is based on a new condenser for somewhere random sources with a special structure. We believe our techniques are interesting in their own right and are promising for further improvement.", acknowledgement = ack-nhfb, } @InProceedings{Rothblum:2013:IPP, author = "Guy N. Rothblum and Salil Vadhan and Avi Wigderson", title = "Interactive proofs of proximity: delegating computation in sublinear time", crossref = "ACM:2013:SPF", pages = "793--802", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488709", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We study interactive proofs with sublinear-time verifiers. These proof systems can be used to ensure approximate correctness for the results of computations delegated to an untrusted server. Following the literature on property testing, we seek proof systems where with high probability the verifier accepts every input in the language, and rejects every input that is far from the language. The verifier's query complexity (and computation complexity), as well as the communication, should all be sublinear. We call such a proof system an Interactive Proof of Proximity (IPP). On the positive side, our main result is that all languages in NC have Interactive Proofs of Proximity with roughly $ \sqrt n $ query and communication and complexities, and $ \polylog (n) $ communication rounds. This is achieved by identifying a natural language, membership in an affine subspace (for a structured class of subspaces), that is complete for constructing interactive proofs of proximity, and providing efficient protocols for it. In building an IPP for this complete language, we show a tradeoff between the query and communication complexity and the number of rounds. For example, we give a 2-round protocol with roughly $ n^{3 / 4} $ queries and communication. On the negative side, we show that there exist natural languages in N$ C^1 $, for which the sum of queries and communication in any constant-round interactive proof of proximity must be polynomially related to $n$. In particular, for any 2-round protocol, the sum of queries and communication must be at least $ \tilde \Omega (\sqrt n) $. Finally, we construct much better IPPs for specific functions, such as bipartiteness on random or well-mixing graphs, and the majority function. The query complexities of these protocols are provably better (by exponential or polynomial factors) than what is possible in the standard property testing model, i.e. without a prover.", acknowledgement = ack-nhfb, } @InProceedings{Ajtai:2013:LBR, author = "Miklos Ajtai", title = "Lower bounds for {RAMs} and quantifier elimination", crossref = "ACM:2013:SPF", pages = "803--812", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488710", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "For each natural number $d$ we consider a finite structure $ M_d $ whose universe is the set of all $ 0, 1 $-sequence of length $ n = 2^d $, each representing a natural number in the set $ \{ 0, 1, \ldots {}, 2^n - 1 \} $ in binary form. The operations included in the structure are the four constants $ 0, 1, 2^n - 1, n $, multiplication and addition modulo $ 2^n $, the unary function $ \{ \min 2^x, 2^n - 1 \} $, the binary functions $ \lfloor x / y \rfloor $ (with $ \lfloor x / 0 \rfloor = 0 $), $ \max (x, y) $, $ \min (x, y) $, and the boolean vector operations, $ {\rm vee} $, $-$ defined on $ 0, 1 $ sequences of length $n$, by performing the operations on all components simultaneously. These are essentially the arithmetic operations that can be performed on a RAM, with wordlength $n$, by a single instruction. We show that there exists an $ \epsilon > 0 $ and a term (that is, an algebraic expression) $ F(x, y) $ built up from the mentioned operations, with the only free variables $x$, $y$, such that if $ G_d(y), d = 0, 1, 2, \ldots {} $, is a sequence of terms, and for all $ d = 0, 1, 2, \ldots {}, M_d $ models $ \forall x, [G_d (x) \to \exists y, F(x, y) = 0] $, then for infinitely many integers $d$, the depth of the term $ G_d $, that is, the maximal number of nestings of the operations in it, is at least $ \epsilon (\log d)^{1 / 2} = \epsilon (\log \log n)^{1 / 2} $. The following is a consequence. We are considering RAMs $ N_n $, with wordlength $ n = 2^d $, whose arithmetic instructions are the arithmetic operations listed above, and also have the usual other RAM instructions. The size of the memory is restricted only by the address space, that is, it is $ 2^n $ words. The RAMs has a finite instruction set, each instruction is encoded by a fixed natural number independently of $n$. Therefore a program $P$ can run on each machine $ N_n $, if $ n = 2^d $ is sufficiently large. We show that there exists an $ \epsilon > 0 $ and a program $P$, such that it satisfies the following two conditions. (i) For all sufficiently large $ n = 2^d $, if $P$ running on N$_n$ gets an input consisting of two words $a$ and $b$, then, in constant time, it gives a $ 0, 1 $ output $ P_n(a, b) $. (ii) Suppose that $Q$ is a program such that for each sufficiently large $ n = 2^d $, if $Q$, running on $ N_n $, gets a word $a$ of length $n$ as an input, then it decides whether there exists a word $b$ of length $n$ such that $ P_n(a, b) = 0. $ Then, for infinitely many positive integers $d$, there exists a word $a$ of length $ n = 2^d $, such that the running time of $Q$ on $ N_n $ at input $a$ is at least $ \epsilon (\log d)^{1 / 2} (\log \log d)^{-1} \geq (\log d)^{1 / 2 - \epsilon } = (\log \log n)^{1 / 2 - \epsilon } $.", acknowledgement = ack-nhfb, } @InProceedings{Beck:2013:STR, author = "Chris Beck and Jakob Nordstrom and Bangsheng Tang", title = "Some trade-off results for polynomial calculus: extended abstract", crossref = "ACM:2013:SPF", pages = "813--822", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488711", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We present size-space trade-offs for the polynomial calculus (PC) and polynomial calculus resolution (PCR) proof systems. These are the first true size-space trade-offs in any algebraic proof system, showing that size and space cannot be simultaneously optimized in these models. We achieve this by extending essentially all known size-space trade-offs for resolution to PC and PCR. As such, our results cover space complexity from constant all the way up to exponential and yield mostly superpolynomial or even exponential size blow-ups. Since the upper bounds in our trade-offs hold for resolution, our work shows that there are formulas for which adding algebraic reasoning on top of resolution does not improve the trade-off properties in any significant way. As byproducts of our analysis, we also obtain trade-offs between space and degree in PC and PCR exactly matching analogous results for space versus width in resolution, and strengthen the resolution trade-offs in [Beame, Beck, and Impagliazzo '12] to apply also to $k$-CNF formulas.", acknowledgement = ack-nhfb, } @InProceedings{Bhowmick:2013:NBM, author = "Abhishek Bhowmick and Zeev Dvir and Shachar Lovett", title = "New bounds for matching vector families", crossref = "ACM:2013:SPF", pages = "823--832", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488713", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "A Matching Vector (MV) family modulo m is a pair of ordered lists $ U = (u_1, \ldots {}, u_t) $ and $ V = (v_1, \ldots {}, v_t) $ where $ u_i, v_j \in Z_m^n $ with the following inner product pattern: for any $ i, \{ u_i, v_i \} = 0 $, and for any $ i \neq j $, $ \{ u_i, v_j \} \neq 0 $. A MV family is called $q$-restricted if inner products $ \{ u_i, v_j \} $ take at most $q$ different values. Our interest in MV families stems from their recent application in the construction of sub-exponential locally decodable codes (LDCs). There, $q$-restricted MV families are used to construct LDCs with $q$ queries, and there is special interest in the regime where $q$ is constant. When $m$ is a prime it is known that such constructions yield codes with exponential block length. However, for composite $m$ the behaviour is dramatically different. A recent work by Efremenko [8] (based on an approach initiated by Yekhanin [24]) gives the first sub-exponential LDC with constant queries. It is based on a construction of a MV family of super-polynomial size by Grolmusz [10] modulo composite $m$. In this work, we prove two lower bounds on the block length of LDCs which are based on black box construction using MV families. When $q$ is constant (or sufficiently small), we prove that such LDCs must have a quadratic block length. When the modulus $m$ is constant (as it is in the construction of Efremenko [8]) we prove a super-polynomial lower bound on the block-length of the LDCs, assuming a well-known conjecture in additive combinatorics, the polynomial Freiman-Ruzsa conjecture over Z$_m$.", acknowledgement = ack-nhfb, } @InProceedings{Ben-Sasson:2013:NFL, author = "Eli Ben-Sasson and Ariel Gabizon and Yohay Kaplan and Swastik Kopparty and Shubangi Saraf", title = "A new family of locally correctable codes based on degree-lifted algebraic geometry codes", crossref = "ACM:2013:SPF", pages = "833--842", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488714", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We describe new constructions of error correcting codes, obtained by ``degree-lifting'' a short algebraic geometry base-code of block-length $q$ to a lifted-code of block-length $ q^m $, for arbitrary integer $m$. The construction generalizes the way degree-d, univariate polynomials evaluated over the $q$-element field (also known as Reed--Solomon codes) are ``lifted'' to degree-d, $m$-variate polynomials (Reed--Muller codes). A number of properties are established: The rate of the degree-lifted code is approximately a 1/m!-fraction of the rate of the base-code. The relative distance of the degree-lifted code is at least as large as that of the base-code. This is proved using a generalization of the Schwartz-Zippel Lemma to degree-lifted Algebraic-Geometry codes. [Local correction] If the base code is invariant under a group that is ``close'' to being doubly-transitive (in a precise manner defined later) then the degree-lifted code is locally correctable with query complexity at most $ q^2 $. The automorphisms of the base-code are crucially used to generate query-sets, abstracting the use of affine-lines in the local correction procedure of Reed--Muller codes. Taking a concrete illustrating example, we show that degree-lifted Hermitian codes form a family of locally correctable codes over an alphabet that is significantly smaller than that obtained by Reed--Muller codes of similar constant rate, message length, and distance.", acknowledgement = ack-nhfb, } @InProceedings{Guruswami:2013:LDR, author = "Venkatesan Guruswami and Chaoping Xing", title = "List decoding {Reed--Solomon}, algebraic-geometric, and {Gabidulin} subcodes up to the singleton bound", crossref = "ACM:2013:SPF", pages = "843--852", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488715", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We consider Reed--Solomon (RS) codes whose evaluation points belong to a subfield, and give a linear-algebraic list decoding algorithm that can correct a fraction of errors approaching the code distance, while pinning down the candidate messages to a well-structured affine space of dimension a constant factor smaller than the code dimension. By pre-coding the message polynomials into a subspace-evasive set, we get a Monte Carlo construction of a subcode of Reed--Solomon codes that can be list decoded from a fraction $ (1 - R - \epsilon) $ of errors in polynomial time (for any fixed $ \epsilon > 0 $) with a list size of $ O(1 / \epsilon) $. Our methods extend to algebraic-geometric (AG) codes, leading to a similar claim over constant-sized alphabets. This matches parameters of recent results based on folded variants of RS and AG codes. but our construction here gives subcodes of Reed--Solomon and AG codes themselves (albeit with restrictions on the evaluation points). Further, the underlying algebraic idea also extends nicely to Gabidulin's construction of rank-metric codes based on linearized polynomials. This gives the first construction of positive rate rank-metric codes list decodable beyond half the distance, and in fact gives codes of rate $R$ list decodable up to the optimal $ (1 - R - \epsilon) $ fraction of rank errors. A similar claim holds for the closely related subspace codes studied by Koetter and Kschischang. We introduce a new notion called subspace designs as another way to pre-code messages and prune the subspace of candidate solutions. Using these, we also get a deterministic construction of a polynomial time list decodable subcode of RS codes. By using a cascade of several subspace designs, we extend our approach to AG codes, which gives the first deterministic construction of an algebraic code family of rate $R$ with efficient list decoding from $ 1 - R - \epsilon $ fraction of errors over an alphabet of constant size (that depends only on $ \epsilon $). The list size bound is almost a constant (governed by $ \log * $ (block length)), and the code can be constructed in quasi-polynomial time.", acknowledgement = ack-nhfb, } @InProceedings{Wootters:2013:LDR, author = "Mary Wootters", title = "On the list decodability of random linear codes with large error rates", crossref = "ACM:2013:SPF", pages = "853--860", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488716", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "It is well known that a random $q$-ary code of rate $ \Omega (\epsilon^2) $ is list decodable up to radius $ (1 - 1 / q - \epsilon) $ with list sizes on the order of $ 1 / \epsilon^2 $, with probability $ 1 - o(1) $. However, until recently, a similar statement about random linear codes has until remained elusive. In a recent paper, Cheraghchi, Guruswami, and Velingker show a connection between list decodability of random linear codes and the Restricted Isometry Property from compressed sensing, and use this connection to prove that a random linear code of rate $ \Omega (\epsilon^2 / \log^3 (1 / \epsilon)) $ achieves the list decoding properties above, with constant probability. We improve on their result to show that in fact we may take the rate to be $ \Omega (\epsilon^2) $, which is optimal, and further that the success probability is $ 1 - o(1) $, rather than constant. As an added benefit, our proof is relatively simple. Finally, we extend our methods to more general ensembles of linear codes. As an example, we show that randomly punctured Reed--Muller codes have the same list decoding properties as the original codes, even when the rate is improved to a constant.", acknowledgement = ack-nhfb, } @InProceedings{Brandao:2013:QFT, author = "Fernando G. S. L. Brandao and Aram W. Harrow", title = "Quantum {de Finetti} theorems under local measurements with applications", crossref = "ACM:2013:SPF", pages = "861--870", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488718", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Quantum de Finetti theorems are a useful tool in the study of correlations in quantum multipartite states. In this paper we prove two new quantum de Finetti theorems, both showing that under tests formed by local measurements in each of the subsystems one can get a much improved error dependence on the dimension of the subsystems. We also obtain similar results for non-signaling probability distributions. We give the following applications of the results to quantum complexity theory, polynomial optimization, and quantum information theory: We prove the optimality of the Chen-Drucker protocol for 3-SAT, under the assumption there is no subexponential-time algorithm for SAT. In the protocol a prover sends to a verifier $ \sqrt n \polylog (n) $ unentangled quantum states, each composed of $ O(\log (n)) $ qubits, as a proof of the satisfiability of a 3-SAT instance with $n$ variables and $ O(n) $ clauses. The quantum verifier checks the validity of the proof by performing local measurements on each of the proofs and classically processing the outcomes. We show that any similar protocol with $ O(n^{1 / 2 - \epsilon }) $ qubits would imply a $ \exp (n^{1 - 2 \epsilon } \polylog (n)) $-time algorithm for 3-SAT. We show that the maximum winning probability of free games (in which the questions to each prover are chosen independently) can be estimated by linear programming in time $ \exp (O(\log |Q| + \log^2 |A| / \epsilon^2)) $, with $ |Q| $ and $ |A| $ the question and answer alphabet sizes, respectively, matching the performance of a previously known algorithm due to Aaronson, Impagliazzo, Moshkovitz, and Shor. This result follows from a new monogamy relation for non-locality, showing that $k$-extendible non-signaling distributions give at most a $ O(k^{-1 / 2}) $ advantage over classical strategies for free games. We also show that 3-SAT with $n$ variables can be reduced to obtaining a constant error approximation of the maximum winning probability under entangled strategies of $ O(\sqrt n) $-player one-round non-local games, in which only two players are selected to send $ O(\sqrt n) $-bit messages. We show that the optimization of certain polynomials over the complex hypersphere can be performed in quasipolynomial time in the number of variables $n$ by considering $ O(\log (n)) $ rounds of the Sum-of-Squares (Parrilo/Lasserre) hierarchy of semidefinite programs. This can be considered an analogue to the hypersphere of a similar known results for the simplex. As an application to entanglement theory, we find a quasipolynomial-time algorithm for deciding multipartite separability. We consider a quantum tomography result due to Aaronson --- showing that given an unknown $n$-qubit state one can perform tomography that works well for most observables by measuring only $ O(n) $ independent and identically distributed (i.i.d.) copies of the state --- and relax the assumption of having i.i.d copies of the state to merely the ability to select subsystems at random from a quantum multipartite state. The proofs of the new quantum de Finetti theorems are based on information theory, in particular on the chain rule of mutual information. The results constitute improvements and generalizations of a recent de Finetti theorem due to Brandao, Christandl and Yard.", acknowledgement = ack-nhfb, } @InProceedings{Brandao:2013:PSA, author = "Fernando G. S. L. Brandao and Aram W. Harrow", title = "Product-state approximations to quantum ground states", crossref = "ACM:2013:SPF", pages = "871--880", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488719", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "The local Hamiltonian problem consists of estimating the ground-state energy (given by the minimum eigenvalue) of a local quantum Hamiltonian. It can be considered as a quantum generalization of constraint satisfaction problems (CSPs) and has a key role in quantum complexity theory, being the first and most natural QMA -complete problem known. An interesting regime for the local Hamiltonian problem is that of extensive error, where one is interested in estimating the mean ground-state energy to constant accuracy. The problem is NP -hard by the PCP theorem, but whether it is QMA -hard is an important open question in quantum complexity theory. A positive solution would represent a quantum analogue of the PCP theorem. A key feature that distinguishes quantum Hamiltonians from classical CSPs is that the solutions may involve complicated entangled states. In this paper, we demonstrate several large classes of Hamiltonians for which product (i.e. unentangled) states can approximate the ground state energy to within a small extensive error. First, we show the mere existence of a good product-state approximation for the ground-state energy of 2-local Hamiltonians with one of more of the following properties: (1) super-constant degree, (2) small expansion, or (3) a ground state with sublinear entanglement with respect to some partition into small pieces. The approximation based on degree is a new and surprising difference between quantum Hamiltonians and classical CSPs, since in the classical setting, higher degree is usually associated with harder CSPs. The approximation based on expansion is not new, but the approximation based on low entanglement was previously known only in the regime where the entanglement was close to zero. Since the existence of a low-energy product state can be checked in NP, this implies that any Hamiltonian used for a quantum PCP theorem should have: (1) constant degree, (2) constant expansion, (3) a ``volume law'' for entanglement with respect to any partition into small parts. Second, we show that in several cases, good product-state approximations not only exist, but can be found in deterministic polynomial time: (1) 2-local Hamiltonians on any planar graph, solving an open problem of Bansal, Bravyi, and Terhal, (2) dense k -local Hamiltonians for any constant k, solving an open problem of Gharibian and Kempe, and (3) 2-local Hamiltonians on graphs with low threshold rank, via a quantum generalization of a recent result of Barak, Raghavendra and Steurer. Our work involves two new tools which may be of independent interest. First, we prove a new quantum version of the de Finetti theorem which does not require the usual assumption of symmetry. Second, we describe a way to analyze the application of the Lasserre/Parrilo SDP hierarchy to local quantum Hamiltonians.", acknowledgement = ack-nhfb, } @InProceedings{Ta-Shma:2013:IWC, author = "Amnon Ta-Shma", title = "Inverting well conditioned matrices in quantum logspace", crossref = "ACM:2013:SPF", pages = "881--890", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488720", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We show that quantum computers improve on the best known classical algorithms for matrix inversion (and singular value decomposition) as far as space is concerned. This adds to the (still short) list of important problems where quantum computers are of help. Specifically, we show that the inverse of a well conditioned matrix can be approximated in quantum logspace with intermediate measurements. This should be compared with the best known classical algorithm for the problem that requires $ \Omega (\log^2 n) $ space. We also show how to approximate the spectrum of a normal matrix, or the singular values of an arbitrary matrix, with $ \epsilon $ additive accuracy, and how to approximate the singular value decomposition (SVD) of a matrix whose singular values are well separated. The technique builds on ideas from several previous works, including simulating Hamiltonians in small quantum space (building on [2] and [10]), treating a Hermitian matrix as a Hamiltonian and running the quantum phase estimation procedure on it (building on [5]) and making small space probabilistic (and quantum) computation consistent through the use of offline randomness and the shift and truncate method (building on [8]).", acknowledgement = ack-nhfb, } @InProceedings{Ambainis:2013:SAE, author = "Andris Ambainis", title = "Superlinear advantage for exact quantum algorithms", crossref = "ACM:2013:SPF", pages = "891--900", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488721", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "A quantum algorithm is exact if, on any input data, it outputs the correct answer with certainty (probability 1). A key question is: how big is the advantage of exact quantum algorithms over their classical counterparts: deterministic algorithms. For total Boolean functions in the query model, the biggest known gap was just a factor of $2$: PARITY of $N$ input bits requires $N$ queries classically but can be computed with $ N / 2 $ queries by an exact quantum algorithm. We present the first example of a Boolean function $ f(x_1, \ldots {}, x_N) $ for which exact quantum algorithms have superlinear advantage over deterministic algorithms. Any deterministic algorithm that computes our function must use $N$ queries but an exact quantum algorithm can compute it with $ O(N^{0.8675 \ldots }) $ queries. A modification of our function gives a similar result for communication complexity: there is a function f which can be computed by an exact quantum protocol that communicates $ O(N^{0.8675 \ldots }) $ quantum bits but requires $ \Omega (N) $ bits of communication for classical protocols.", acknowledgement = ack-nhfb, } @InProceedings{Li:2013:AKM, author = "Shi Li and Ola Svensson", title = "Approximating $k$-median via pseudo-approximation", crossref = "ACM:2013:SPF", pages = "901--910", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488723", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We present a novel approximation algorithm for $k$-median that achieves an approximation guarantee of $ 1 + \sqrt 3 + \epsilon $ , improving upon the decade-old ratio of $ 3 + \epsilon $ . Our approach is based on two components, each of which, we believe, is of independent interest. First, we show that in order to give an $ \alpha $ -approximation algorithm for $k$-median, it is sufficient to give a pseudo-approximation algorithm that finds an $ \alpha $-approximate solution by opening $ k + O(1) $ facilities. This is a rather surprising result as there exist instances for which opening $ k + 1 $ facilities may lead to a significant smaller cost than if only $k$ facilities were opened. Second, we give such a pseudo-approximation algorithm with $ \alpha = 1 + \sqrt 3 + \epsilon $. Prior to our work, it was not even known whether opening $ k + o(k) $ facilities would help improve the approximation ratio.", acknowledgement = ack-nhfb, } @InProceedings{Kelner:2013:SCA, author = "Jonathan A. Kelner and Lorenzo Orecchia and Aaron Sidford and Zeyuan Allen Zhu", title = "A simple, combinatorial algorithm for solving {SDD} systems in nearly-linear time", crossref = "ACM:2013:SPF", pages = "911--920", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488724", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "In this paper, we present a simple combinatorial algorithm that solves symmetric diagonally dominant (SDD) linear systems in nearly-linear time. It uses little of the machinery that previously appeared to be necessary for a such an algorithm. It does not require recursive preconditioning, spectral sparsification, or even the Chebyshev Method or Conjugate Gradient. After constructing a ``nice'' spanning tree of a graph associated with the linear system, the entire algorithm consists of the repeated application of a simple update rule, which it implements using a lightweight data structure. The algorithm is numerically stable and can be implemented without the increased bit-precision required by previous solvers. As such, the algorithm has the fastest known running time under the standard unit-cost RAM model. We hope the simplicity of the algorithm and the insights yielded by its analysis will be useful in both theory and practice.", acknowledgement = ack-nhfb, } @InProceedings{Sherstov:2013:CLB, author = "Alexander A. Sherstov", title = "Communication lower bounds using directional derivatives", crossref = "ACM:2013:SPF", pages = "921--930", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488725", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We study the set disjointness problem in the most powerful bounded-error model: the number-on-the-forehead model with $k$ parties and arbitrary classical or quantum communication. We obtain a communication lower bound of $ \Omega (\sqrt (n) / 2^k *k) $ bits, which is essentially optimal. Proving it was a longstanding open problem even in restricted settings, such as one-way classical protocols with $ k = 4 $ parties (Wigderson 1997). The proof contributes a novel technique for lower bounds on multiparty communication, based on directional derivatives of communication protocols over the reals.", acknowledgement = ack-nhfb, } @InProceedings{Andoni:2013:HFU, author = "Alexandr Andoni and Assaf Goldberger and Andrew McGregor and Ely Porat", title = "Homomorphic fingerprints under misalignments: sketching edit and shift distances", crossref = "ACM:2013:SPF", pages = "931--940", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488726", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "Fingerprinting is a widely-used technique for efficiently verifying that two files are identical. More generally, linear sketching is a form of lossy compression (based on random projections) that also enables the ``dissimilarity'' of non-identical files to be estimated. Many sketches have been proposed for dissimilarity measures that decompose coordinate-wise such as the Hamming distance between alphanumeric strings, or the Euclidean distance between vectors. However, virtually nothing is known on sketches that would accommodate alignment errors. With such errors, Hamming or Euclidean distances are rendered useless: a small misalignment may result in a file that looks very dissimilar to the original file according such measures. In this paper, we present the first linear sketch that is robust to a small number of alignment errors. Specifically, the sketch can be used to determine whether two files are within a small Hamming distance of being a cyclic shift of each other. Furthermore, the sketch is homomorphic with respect to rotations: it is possible to construct the sketch of a cyclic shift of a file given only the sketch of the original file. The relevant dissimilarity measure, known as the shift distance, arises in the context of embedding edit distance and our result addressed an open problem [Question 13 in Indyk-McGregor-Newman-Onak'11] with a rather surprising outcome. Our sketch projects a length $n$ file into $ D(n) \cdot \polylog n $ dimensions where $ D(n)l n $ is the number of divisors of $n$. The striking fact is that this is near-optimal, i.e., the $ D(n) $ dependence is inherent to a problem that is ostensibly about lossy compression. In contrast, we then show that any sketch for estimating the edit distance between two files, even when small, requires sketches whose size is nearly linear in $n$. This lower bound addresses a long-standing open problem on the low distortion embeddings of edit distance [Question 2.15 in Naor-Matousek'11, Indyk'01], for the case of linear embeddings.", acknowledgement = ack-nhfb, } @InProceedings{Chonev:2013:OPH, author = "Ventsislav Chonev and Jo{\"e}l Ouaknine and James Worrell", title = "The orbit problem in higher dimensions", crossref = "ACM:2013:SPF", pages = "941--950", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488728", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We consider higher-dimensional versions of Kannan and Lipton's Orbit Problem---determining whether a target vector space V may be reached from a starting point x under repeated applications of a linear transformation A. Answering two questions posed by Kannan and Lipton in the 1980s, we show that when V has dimension one, this problem is solvable in polynomial time, and when V has dimension two or three, the problem is in NP$^{RP}$.", acknowledgement = ack-nhfb, } @InProceedings{Azar:2013:LSD, author = "Yossi Azar and Ilan Reuven Cohen and Iftah Gamzu", title = "The loss of serving in the dark", crossref = "ACM:2013:SPF", pages = "951--960", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488729", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We study the following balls and bins stochastic process: There is a buffer with B bins, and there is a stream of balls X = {X$_1$, X$_2$, \ldots{} ,X$_T$ } such that X$_i$ is the number of balls that arrive before time i but after time i-1. Once a ball arrives, it is stored in one of the unoccupied bins. If all the bins are occupied then the ball is thrown away. In each time step, we select a bin uniformly at random, clear it, and gain its content. Once the stream of balls ends, all the remaining balls in the buffer are cleared and added to our gain. We are interested in analyzing the expected gain of this randomized process with respect to that of an optimal gain-maximizing strategy, which gets the same online stream of balls, and clears a ball from a bin, if exists, at any step. We name this gain ratio the loss of serving in the dark. In this paper, we determine the exact loss of serving in the dark. We prove that the expected gain of the randomized process is worse by a factor of $ \rho + \epsilon $ from that of the optimal gain-maximizing strategy for any $ \epsilon > 0 $, where $ \rho = \max_{ \alpha > 1} \alpha e^{ \alpha } / ((\alpha - 1)e^{ \alpha } + e - 1) \sim 1.69996 $ and $ B = \Omega (1 / \epsilon^3) $. We also demonstrate that this bound is essentially tight as there are specific ball streams for which the above-mentioned gain ratio tends to $ \rho $. Our stochastic process occurs naturally in many applications. We present a prompt and truthful mechanism for bounded capacity auctions, and an application relating to packets scheduling.", acknowledgement = ack-nhfb, } @InProceedings{Azar:2013:TBO, author = "Yossi Azar and Ilan Reuven Cohen and Seny Kamara and Bruce Shepherd", title = "Tight bounds for online vector bin packing", crossref = "ACM:2013:SPF", pages = "961--970", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488730", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "In the $d$-dimensional bin packing problem (VBP), one is given vectors $ x_1, x_2, \ldots {}, x_n \in R^d $ and the goal is to find a partition into a minimum number of feasible sets: $ \{ 1, 2, \ldots {}, n \} = \cup_i^s B_i $. A set $ B_i $ is feasible if $ \Sigma_{j \in B i} x_j \leq 1 $, where $1$ denotes the all $1$'s vector. For online VBP, it has been outstanding for almost 20 years to clarify the gap between the best lower bound $ \Omega (1) $ on the competitive ratio versus the best upper bound of $ O(d) $. We settle this by describing a $ \Omega (d^{1 - \epsilon }) $ lower bound. We also give strong lower bounds (of $ \Omega (d^{1 / B - \epsilon }) $) if the bin size $ B \in Z_+ $ is allowed to grow. Finally, we discuss almost-matching upper bound results for general values of $B$; we show an upper bound whose exponent is additively ``shifted by 1'' from the lower bound exponent.", acknowledgement = ack-nhfb, } @InProceedings{Li:2013:SCO, author = "Jian Li and Wen Yuan", title = "Stochastic combinatorial optimization via {Poisson} approximation", crossref = "ACM:2013:SPF", pages = "971--980", year = "2013", DOI = "https://doi.org/10.1145/2488608.2488731", bibdate = "Mon Mar 3 06:30:33 MST 2014", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", abstract = "We study several stochastic combinatorial problems, including the expected utility maximization problem, the stochastic knapsack problem and the stochastic bin packing problem. A common technical challenge in these problems is to optimize some function (other than the expectation) of the sum of a set of random variables. The difficulty is mainly due to the fact that the probability distribution of the sum is the convolution of a set of distributions, which is not an easy objective function to work with. To tackle this difficulty, we introduce the Poisson approximation technique. The technique is based on the Poisson approximation theorem discovered by Le Cam, which enables us to approximate the distribution of the sum of a set of random variables using a compound Poisson distribution. Using the technique, we can reduce a variety of stochastic problems to the corresponding deterministic multiple-objective problems, which either can be solved by standard dynamic programming or have known solutions in the literature. For the problems mentioned above, we obtain the following results: We first study the expected utility maximization problem introduced recently [Li and Despande, FOCS11]. For monotone and Lipschitz utility functions, we obtain an additive PTAS if there is a multidimensional PTAS for the multi-objective version of the problem, strictly generalizing the previous result. The result implies the first additive PTAS for maximizing threshold probability for the stochastic versions of global min-cut, matroid base and matroid intersection. For the stochastic bin packing problem (introduced in [Kleinberg, Rabani and Tardos, STOC97]), we show there is a polynomial time algorithm which uses at most the optimal number of bins, if we relax the size of each bin and the overflow probability by e for any constant $ \epsilon > 0 $. Based on this result, we obtain a 3-approximation if only the size of each bin can be relaxed by $ \epsilon $ , improving the known $ O(1 / \epsilon) $ factor for constant overflow probability. For stochastic knapsack, we show a $ (1 + \epsilon) $-approximation using $ \epsilon $ extra capacity for any $ \epsilon > 0 $, even when the size and reward of each item may be correlated and cancelations of items are allowed. This generalizes the previous work [Balghat, Goel and Khanna, SODA11] for the case without correlation and cancelation. Our algorithm is also simpler. We also present a factor $ 2 + \epsilon $ approximation algorithm for stochastic knapsack with cancelations, for any constant $ \epsilon > 0 $, improving the current known approximation factor of 8 [Gupta, Krishnaswamy, Molinaro and Ravi, FOCS11]. We also study an interesting variant of the stochastic knapsack problem, where the size and the profit of each item are revealed before the decision is made. The problem falls into the framework of Bayesian online selection problems, which has been studied a lot recently.", acknowledgement = ack-nhfb, }

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@Proceedings{ACM:2006:SPT, editor = "{ACM}", booktitle = "{STOC'06: Proceedings of the Thirty-Eighth Annual ACM Symposium on Theory of Computing 2006, Seattle, WA, USA, May 21--23, 2006}", title = "{STOC'06: Proceedings of the Thirty-Eighth Annual ACM Symposium on Theory of Computing 2006, Seattle, WA, USA, May 21--23, 2006}", publisher = pub-ACM, address = pub-ACM:adr, pages = "770 (est.)", year = "2006", ISBN = "1-59593-134-1", ISBN-13 = "978-1-59593-134-4", LCCN = "QA75.5 .A22 2006", bibdate = "Thu May 25 06:13:58 2006", bibsource = "http://www.math.utah.edu/pub/tex/bib/stoc.bib; http://www.math.utah.edu/pub/tex/bib/stoc2000.bib; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib; z3950.gbv.de:20011/gvk", note = "ACM order number 508060.", URL = "http://portal.acm.org/citation.cfm?id=1132516", acknowledgement = ack-nhfb, } @Proceedings{ACM:2010:SPA, editor = "{ACM}", booktitle = "{STOC'10: Proceedings of the 2010 ACM International Symposium on Theory of Computing: June 5--8, 2010, Cambridge, MA, USA}", title = "{STOC'10: Proceedings of the 2010 ACM International Symposium on Theory of Computing: June 5--8, 2010, Cambridge, MA, USA}", publisher = pub-ACM, address = pub-ACM:adr, pages = "xiv + 797", year = "2010", ISBN = "1-60558-817-2", ISBN-13 = "978-1-60558-817-9", LCCN = "QA 76.6 .A152 2010", bibdate = "Wed Sep 1 10:37:53 MDT 2010", bibsource = "z3950.gbv.de:20011/gvk; http://www.math.utah.edu/pub/tex/bib/stoc.bib; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", URL = "http://www.gbv.de/dms/tib-ub-hannover/63314455x.", acknowledgement = ack-nhfb, remark = "42nd annual STOC meeting.", } @Proceedings{ACM:2011:SPA, editor = "{ACM}", booktitle = "{STOC'11: Proceedings of the 2011 ACM International Symposium on Theory of Computing: June 6--8, 2011, San Jose, CA, USA}", title = "{STOC'11: Proceedings of the 2011 ACM International Symposium on Theory of Computing: June 6--8, 2011, San Jose, CA, USA}", publisher = pub-ACM, address = pub-ACM:adr, pages = "xxx + 822 (est.)", year = "2011", ISBN = "1-4503-0691-8", ISBN-13 = "978-1-4503-0691-1", LCCN = "????", bibdate = "Wed Sep 1 10:37:53 MDT 2010", bibsource = "z3950.gbv.de:20011/gvk; http://www.math.utah.edu/pub/tex/bib/stoc.bib; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", URL = "http://www.gbv.de/dms/tib-ub-hannover/63314455x.", acknowledgement = ack-nhfb, remark = "43rd annual STOC meeting.", } @Proceedings{ACM:2012:SPA, editor = "{ACM}", booktitle = "{STOC'12: Proceedings of the 2012 ACM International Symposium on Theory of Computing: May 19--22, 2012, New York, NY, USA}", title = "{STOC'12: Proceedings of the 2012 ACM International Symposium on Theory of Computing: May 19--22, 2012, New York, NY, USA}", publisher = pub-ACM, address = pub-ACM:adr, pages = "1292 (est.)", year = "2012", ISBN = "1-4503-1245-4", ISBN-13 = "978-1-4503-1245-5", LCCN = "????", bibdate = "Thu Nov 08 19:12:21 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/stoc2010.bib; http://www.math.utah.edu/pub/tex/bib/stoc.bib; z3950.gbv.de:20011/gvk", URL = "http://www.gbv.de/dms/tib-ub-hannover/63314455x.", acknowledgement = ack-nhfb, remark = "44th annual STOC meeting.", } @Proceedings{ACM:2013:SPF, editor = "{ACM}", booktitle = "{STOC '13: Proceedings of the Forty-fifth Annual ACM Symposium on Theory of Computing: June 1--4, 2013, Palo Alto, California, USA}", title = "{STOC '13: Proceedings of the Forty-fifth Annual ACM Symposium on Theory of Computing: June 1--4, 2013, Palo Alto, California, USA}", publisher = pub-ACM, address = pub-ACM:adr, pages = "980 (est.)", year = "2013", ISBN = "1-4503-2029-5", ISBN-13 = "978-1-4503-2029-0", bibdate = "Mon Mar 3 06:36:05 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/datacompression.bib; http://www.math.utah.edu/pub/tex/bib/prng.bib; http://www.math.utah.edu/pub/tex/bib/stoc.bib; http://www.math.utah.edu/pub/tex/bib/stoc2010.bib", acknowledgement = ack-nhfb, remark = "45th annual STOC meeting.", }