Entry Narlikar:1999:SES from toplas.bib
Last update: Tue May 1 02:05:46 MDT 2012
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BibTeX entry
@Article{Narlikar:1999:SES,
author = "Girija J. Narlikar and Guy E. Blelloch",
title = "Space-Efficient Scheduling of Nested Parallelism",
journal = j-TOPLAS,
volume = "21",
number = "1",
pages = "138--173",
month = jan,
year = "1999",
CODEN = "ATPSDT",
ISSN = "0164-0925 (print), 1558-4593 (electronic)",
ISSN-L = "0164-0925",
bibdate = "Tue Sep 26 10:12:58 MDT 2000",
bibsource = "http://www.acm.org/pubs/contents/journals/toplas/;
http://www.math.utah.edu/pub/tex/bib/toplas.bib",
URL = "http://www.acm.org/pubs/citations/journals/toplas/1999-21-1/p138-narlikar/",
abstract = "Many of today's high-level parallel languages support
dynamic, fine-grained parallelism. These languages
allow the user to expose all the parallelism in the
program, which is typically of a much higher degree
than the number of processors. Hence an efficient
scheduling algorithm is required to assign computations
to processors at runtime. Besides having low overheads
and good load balancing, it is important for the
scheduling algorithm to minimize the space usage of the
parallel program. This article presents an on-line
scheduling algorithm that is provably space efficient
and time efficient for nested-parallel languages. For a
computation with depth $D$ and serial space requirement
$S_1$, the algorithm generates a schedule that requires
at most $S_1 + O(K\cdot D\cdot p)$ space (including
scheduler space) on $p$ processors. Here, $K$ is a
user-adjustable runtime parameter specifying the net
amount of memory that a thread may allocate before it
is preempted by the scheduler. Adjusting the value of
$K$ provides a trade-off between the running time and
the memory requirement of a parallel computation. To
allow the scheduler to scale with the number of
processors we also parallelize the scheduler and
analyze the space and time bounds of the computation to
include scheduling costs. In addition to showing that
the scheduling algorithm is space and time efficient in
theory, we demonstrate that it is effective in
practice. We have implemented a runtime system that
uses our algorithm to schedule lightweight parallel
threads. The results of executing parallel programs on
this system show that our scheduling algorithm
significantly reduces memory usage compared to previous
techniques, without compromising performance.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Programming Languages and
Systems",
generalterms = "Algorithms; Languages; Performance",
keywords = "dynamic scheduling; multithreading; nested
parallelism; parallel language implementation; space
efficiency",
subject = "Software --- Programming Techniques --- Concurrent
Programming (D.1.3): {\bf Parallel programming};
Software --- Programming Languages --- Processors
(D.3.4): {\bf Run-time environments}; Theory of
Computation --- Analysis of Algorithms and Problem
Complexity --- General (F.2.0)",
}
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- $p$,
16(4)1215,
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4(4)563,
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4(1)44,
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16(6)1811,
17(1)47,
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17(3)431,
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22(5)861,
27(6)1147,
28(1)1,
28(1)175,
28(2)331,
28(3)389,
28(4)696,
28(4)747,
28(5)848,
28(5)942,
29(2)13,
29(5)29,
30(2)8,
30(5)25,
30(6)30,
30(6)33,
31(1)1,
31(1)4,
31(3)10,
31(3)12,
31(6)20,
31(6)21,
32(1)1,
32(1)2,
32(3)9,
33(1)4,
34(1)1,
34(1)4
- allocate,
9(2)235,
13(1)1,
21(5)895
- allow,
3(2)126,
4(3)455,
4(4)687,
5(2)127,
5(3)405,
6(4)546,
7(1)159,
8(4)419,
8(4)547,
9(2)164,
9(2)235,
9(3)319,
9(3)367,
9(4)473,
10(2)189,
12(4)643,
13(2)237,
13(2)269,
14(1)54,
14(2)265,
14(4)490,
16(3)577,
16(3)687,
16(3)924,
16(3)954,
16(3)1051,
16(4)1279,
16(5)1411,
16(6)1661,
16(6)1811,
17(4)561,
18(5)564,
18(5)615,
19(1)7,
19(1)153,
19(4)557,
20(1)208,
20(4)869,
20(5)980,
20(6)1223,
21(1)46,
21(2)324,
21(4)703,
22(2)296,
22(3)471,
22(4)673,
22(6)1002,
22(6)1037,
27(6)1049,
27(6)1216,
27(6)1344,
28(1)1,
28(3)517,
28(4)715,
28(5)942,
29(6)35,
30(4)18,
30(4)22,
31(2)8,
31(3)12,
32(2)4,
32(3)9,
32(4)11,
32(5)19,
33(1)4,
34(1)6
- amount,
8(1)109,
16(3)328,
16(3)428,
16(4)1156,
17(4)600,
18(4)477,
20(2)344,
20(3)635,
21(4)703,
22(2)378,
28(3)429,
28(5)908,
34(1)4
- analyze,
4(1)44,
10(2)248,
14(1)54,
16(3)1051,
18(5)564,
18(6)659,
19(1)153,
19(5)639,
19(6)942,
20(5)917,
21(1)11,
21(6)1196,
22(2)187,
26(2)263,
29(1)3,
32(4)13,
32(6)23
- balancing,
16(3)577,
20(5)980,
27(6)1097
- Besides,
30(5)26,
30(6)32
- Blelloch, Guy E.,
21(2)240,
28(6)990,
32(1)3
- bound,
9(2)235,
13(2)211,
16(3)607,
16(4)1248,
16(5)1472,
17(2)197,
18(1)1,
19(6)899,
20(1)208,
20(3)635,
20(6)1171,
21(2)240,
22(1)1,
22(1)87,
22(2)265,
22(5)773,
27(2)185,
27(3)388,
27(3)527,
28(4)577,
29(5)28,
29(6)38,
30(1)4,
30(5)26,
32(5)18,
32(6)21,
34(1)2,
34(1)6
- compared,
4(1)21,
6(4)546,
13(1)150,
16(1)35,
16(5)1431,
17(4)635,
17(5)740,
19(1)188,
19(6)992,
20(1)166,
20(3)586,
20(6)1265,
27(6)1097,
28(3)476,
28(4)577,
28(5)908,
30(3)17,
30(4)23,
30(6)33,
31(2)8,
32(1)3,
32(4)13
- complexity,
3(2)126,
4(2)258,
7(4)501,
8(1)109,
10(2)248,
13(2)211,
14(3)339,
15(4)632,
15(5)826,
16(1)35,
16(3)1051,
16(5)1472,
16(5)1512,
17(2)228,
17(2)331,
17(3)535,
17(4)600,
17(4)635,
18(3)268,
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19(1)1,
20(1)1,
20(1)116,
20(2)274,
20(2)344,
20(3)586,
20(3)635,
21(1)90,
21(3)417,
21(3)502,
21(4)790,
21(4)813,
22(1)87,
22(5)816,
27(6)1270,
28(1)175,
30(3)13,
30(4)23,
31(2)8,
31(4)16,
31(6)21,
32(4)14,
32(4)15,
32(6)21,
33(6)21
- cost,
3(4)508,
6(2)159,
8(4)491,
11(4)491,
14(1)28,
14(4)490,
15(5)826,
16(3)428,
16(3)775,
16(4)1319,
16(5)1449,
17(1)123,
18(3)268,
18(4)424,
18(6)683,
19(6)992,
20(1)166,
20(2)274,
20(4)869,
20(6)1223,
20(6)1297,
21(2)189,
21(2)240,
21(3)502,
21(5)914,
21(5)977,
22(2)296,
22(5)932,
22(6)973,
23(2)105,
27(4)631,
27(5)946,
27(6)1049,
27(6)1270,
29(1)2,
30(6)31,
31(3)9,
31(5)17,
32(4)11
- d.1.3,
7(1)80,
7(2)244,
7(2)270,
7(2)311,
7(3)380,
7(3)404,
7(4)501,
7(4)622,
8(1)88,
8(1)109,
8(1)140,
8(1)142,
8(1)154,
8(3)326,
8(3)388,
9(1)25,
9(2)235,
9(3)350,
9(4)491,
10(1)51,
10(3)420,
10(4)513,
11(1)147,
12(3)396,
12(3)463,
12(4)643,
13(4)491,
14(1)54,
14(2)201,
14(3)396,
15(1)1,
15(1)73,
15(2)337,
15(3)563,
15(5)745,
15(5)771,
16(3)524,
16(3)577,
16(3)649,
16(3)798,
16(3)954,
16(6)1737,
17(2)233,
17(3)535,
17(5)704,
18(5)615,
19(2)292,
19(3)444,
19(5)685,
19(5)804,
20(1)51,
20(3)483,
20(6)1131,
20(6)1171,
20(6)1195,
21(1)11,
21(1)46,
21(2)189,
21(3)569,
22(2)265,
22(2)296,
22(2)416,
22(4)673
- degree,
16(5)1431,
17(2)264,
17(2)331,
18(1)30,
18(6)659,
21(2)240,
27(6)1147
- demonstrate,
7(4)560,
9(2)125,
11(4)598,
13(1)52,
14(4)471,
16(3)305,
16(3)328,
16(3)649,
16(3)843,
16(3)986,
16(5)1512,
17(2)197,
17(5)777,
19(5)751,
19(6)1053,
20(1)116,
20(2)436,
20(6)1195,
21(3)627,
21(4)747,
22(2)224,
22(3)471,
22(3)540,
22(6)1037,
23(2)105,
28(1)1,
28(2)207,
28(5)908,
29(1)2,
30(2)8,
31(2)6,
31(3)9,
31(3)12,
31(4)14,
32(2)4,
32(3)7,
32(3)9
- depth,
6(4)632,
15(1)133,
16(5)1472,
18(4)424,
20(1)208,
21(2)240,
27(6)1147,
31(4)13
- effective,
5(2)223,
6(1)55,
9(3)367,
16(3)370,
16(4)1279,
16(6)1811,
17(1)85,
17(2)394,
18(4)424,
18(4)477,
19(1)188,
19(5)751,
20(1)166,
20(4)845,
20(5)980,
21(4)703,
21(6)1251,
24(6)667,
27(3)527,
28(1)106,
28(1)134,
28(4)715,
30(3)17,
30(4)23,
32(1)3,
32(2)6,
32(6)24,
33(6)19
- efficiency,
3(2)126,
4(4)650,
8(4)577,
9(2)164,
9(4)473,
11(4)598,
13(1)21,
13(1)52,
14(1)28,
16(3)687,
16(3)798,
16(3)1051,
16(4)1081,
16(6)1675,
17(1)28,
18(1)30,
18(2)175,
18(5)528,
18(6)659,
19(1)153,
20(1)116,
20(6)1195,
20(6)1223,
21(1)1,
21(3)627,
21(4)703,
21(4)848,
21(5)977,
21(6)1137,
22(2)296,
27(6)1097,
30(1)4,
30(5)28,
31(1)2,
32(6)21,
33(1)3,
34(1)3,
34(1)5
- Efficient, Space-,
3(4)388
- executing,
14(1)54,
18(5)528,
18(6)659,
20(6)1131,
20(6)1195,
22(3)471,
28(5)908,
29(1)2,
30(2)8,
32(4)12,
32(6)24,
34(1)6
- expose,
16(4)1248,
28(1)134,
28(1)175,
28(3)476
- F.2.0,
17(6)805,
21(3)417
- fine-grained,
11(4)598,
22(3)540,
28(2)331
- generate,
4(1)21,
5(2)127,
8(4)577,
9(2)235,
9(3)297,
9(4)473,
12(4)643,
13(1)1,
14(2)147,
16(3)328,
16(3)1010,
16(4)1279,
17(2)181,
17(2)217,
17(2)264,
17(2)293,
17(3)461,
19(1)48,
19(3)492,
19(6)942,
20(4)869,
20(5)980,
21(2)286,
21(2)324,
21(2)370,
21(4)703,
21(6)1077,
22(4)583,
22(6)973,
28(3)476,
29(6)33,
30(3)17,
30(4)22,
31(5)18,
34(1)3,
34(1)5
- good,
7(1)62,
9(2)235,
14(2)173,
14(4)574,
16(3)328,
17(2)181,
18(4)401,
20(4)869,
20(6)1195,
21(2)370,
21(3)677,
21(4)703,
22(1)129,
22(2)224,
22(5)932,
27(6)1097,
30(5)29,
31(6)20,
32(6)23
- grained, fine-,
11(4)598,
22(3)540,
28(2)331
- having,
4(2)258,
5(2)236,
14(1)54,
14(2)173,
14(4)589,
18(2)175,
18(5)615,
19(3)462,
20(1)51,
20(1)208,
21(2)240,
21(3)502,
21(4)790,
22(2)378,
32(6)23
- hence,
14(2)127,
16(5)1449,
18(3)235,
20(4)869,
21(4)703,
27(6)1270,
32(3)8
- here,
4(1)113,
4(2)258,
4(4)601,
4(4)615,
9(4)491,
10(2)189,
10(2)204,
14(1)28,
15(4)575,
15(5)876,
16(4)1361,
16(5)1431,
16(5)1613,
16(6)1699,
18(2)109,
18(4)355,
19(4)586,
20(5)1014,
22(6)1002,
28(4)747,
29(5)29,
30(3)12,
32(1)2,
33(1)4
- high-level,
4(1)44,
4(2)149,
4(2)226,
4(3)402,
4(4)650,
6(4)546,
9(2)198,
9(2)257,
9(3)367,
14(3)299,
16(5)1613,
18(2)139,
21(2)286,
21(2)324,
21(3)527,
22(4)583,
22(4)701,
25(6)814,
30(4)18,
30(4)19,
30(6)32,
31(2)8,
31(6)22,
32(3)9,
32(4)12
- higher,
13(2)269,
14(3)299,
14(3)339,
16(6)1811,
18(6)659,
30(6)31
- implemented,
4(2)149,
4(2)295,
7(1)137,
7(3)404,
7(4)501,
8(3)344,
9(2)235,
13(1)1,
14(2)147,
14(4)471,
15(1)182,
16(2)175,
16(3)577,
16(3)843,
16(3)986,
16(4)1248,
16(4)1319,
16(5)1431,
16(5)1512,
16(6)1699,
17(1)85,
17(2)197,
17(2)233,
17(4)635,
18(3)268,
18(4)424,
18(5)528,
18(5)564,
18(5)615,
18(6)752,
19(1)153,
19(5)726,
19(5)804,
19(6)942,
20(3)483,
20(4)869,
20(5)1014,
20(6)1195,
20(6)1265,
21(4)703,
22(2)378,
22(5)816,
27(6)1049,
27(6)1097,
28(1)1,
28(1)70,
28(1)106,
28(1)134,
28(2)207,
28(4)696,
29(1)3,
29(5)29,
30(3)17,
30(4)22,
30(4)23,
31(1)1,
31(2)6,
31(2)8,
31(6)22,
32(2)4,
32(5)16,
32(5)18,
32(6)21,
34(1)2
- important,
4(2)179,
4(3)455,
4(4)527,
4(4)687,
9(2)125,
13(1)21,
14(3)339,
14(4)521,
15(4)659,
15(5)771,
16(2)205,
16(3)986,
16(4)1081,
16(4)1156,
16(4)1319,
16(6)1811,
17(4)600,
18(3)300,
18(4)454,
18(4)477,
19(1)188,
20(1)51,
20(3)586,
20(6)1223,
21(2)189,
21(2)324,
21(5)914,
21(5)977,
21(6)1251,
22(3)506,
22(4)638,
22(4)701,
22(6)1002,
27(6)1049,
28(4)747,
29(1)3,
30(2)8,
30(3)17,
30(4)18,
30(6)33,
30(6)34,
32(3)8,
32(3)9,
34(1)2,
34(1)3,
34(1)5
- include,
4(2)149,
4(2)226,
4(4)552,
4(4)711,
4(4)733,
5(2)127,
8(4)419,
9(2)125,
12(4)643,
13(2)237,
15(4)681,
15(5)771,
16(3)605,
16(5)1472,
16(6)1675,
17(5)777,
18(2)139,
19(3)492,
19(5)685,
19(6)992,
19(6)1053,
21(2)370,
21(3)430,
21(4)848,
21(6)1196,
22(4)673,
22(5)932,
22(6)973,
27(6)1097,
27(6)1147,
28(1)1,
28(4)577,
29(1)2,
30(4)18,
30(5)28,
31(2)7,
32(2)4,
32(3)7
- including,
4(3)402,
4(4)552,
4(4)585,
6(2)159,
7(1)159,
7(4)501,
7(4)560,
8(4)419,
9(2)235,
14(1)28,
15(1)36,
16(2)175,
16(3)577,
16(3)687,
16(3)798,
16(3)954,
16(5)1512,
16(5)1572,
16(5)1613,
17(1)85,
17(2)293,
17(4)600,
18(2)109,
18(2)175,
19(1)87,
19(3)413,
19(6)899,
19(6)1053,
20(5)1014,
21(2)240,
21(3)527,
21(4)703,
21(6)1251,
22(6)1037,
28(3)517,
30(4)19,
30(6)33,
31(2)7,
31(4)16,
32(4)11,
32(4)15,
33(1)5,
34(1)3
- level, high-,
4(1)44,
4(2)149,
4(2)226,
4(3)402,
4(4)650,
6(4)546,
9(2)198,
9(2)257,
9(3)367,
14(3)299,
16(5)1613,
18(2)139,
21(2)286,
21(2)324,
21(3)527,
22(4)583,
22(4)701,
25(6)814,
30(4)18,
30(4)19,
30(6)32,
31(2)8,
31(6)22,
32(3)9,
32(4)12
- lightweight,
17(5)704,
19(1)48
- line, on-,
16(5)1399,
20(1)208,
21(3)569,
31(6)20
- load,
16(3)577,
17(5)740,
18(6)659,
22(3)490,
22(5)932,
27(6)1097
- low,
19(6)853,
20(6)1265,
22(5)932,
27(6)1049,
28(1)1,
31(5)17,
32(4)11,
32(4)12,
32(6)23,
34(1)4
- many,
4(1)21,
4(1)44,
4(1)83,
4(3)455,
4(4)552,
4(4)563,
4(4)687,
7(2)183,
9(2)125,
9(2)235,
9(2)257,
9(3)319,
13(1)21,
13(1)124,
13(2)211,
14(1)1,
14(4)471,
14(4)490,
16(1)35,
16(2)175,
16(3)305,
16(3)387,
16(4)1248,
16(5)1399,
16(5)1411,
16(5)1431,
16(6)1737,
17(1)63,
17(2)181,
17(5)777,
18(1)30,
18(1)73,
18(3)254,
18(3)300,
18(5)528,
18(5)615,
19(4)568,
20(1)51,
20(1)208,
20(3)635,
20(6)1111,
20(6)1131,
21(2)324,
21(3)502,
21(3)527,
21(3)677,
21(4)703,
21(4)747,
22(2)187,
22(2)265,
27(6)1049,
27(6)1216,
27(6)1270,
28(1)70,
28(1)106,
28(2)207,
28(4)747,
30(2)8,
30(3)12,
30(4)18,
30(6)33,
30(6)34,
31(1)3,
31(2)6,
31(3)9,
31(6)20,
32(1)3,
32(5)19,
32(6)22,
33(3)10,
34(1)2,
34(1)3
- may,
4(1)83,
4(2)125,
4(3)382,
4(3)496,
4(4)563,
5(3)405,
6(2)159,
9(3)408,
13(2)181,
14(2)201,
15(4)706,
15(5)876,
16(1)151,
16(3)524,
16(3)607,
16(3)649,
16(3)798,
16(3)1010,
16(3)1024,
16(4)1156,
16(4)1248,
16(5)1431,
16(5)1449,
16(6)1675,
16(6)1699,
17(2)181,
17(2)217,
17(3)448,
17(4)635,
17(5)777,
18(1)73,
18(2)109,
18(2)139,
18(6)752,
19(1)48,
19(3)525,
19(4)617,
20(1)208,
20(4)724,
20(4)869,
20(6)1131,
21(1)1,
21(1)11,
21(3)430,
21(3)502,
21(3)677,
21(6)1196,
22(2)296,
22(2)416,
22(4)701,
27(6)1049,
27(6)1344,
28(2)290,
28(2)331,
28(5)795,
28(5)908,
28(5)942,
30(3)12,
30(4)21,
30(5)29,
31(3)11,
31(5)17,
31(6)20,
31(6)21,
32(1)2,
32(3)9,
32(4)13,
32(4)15,
32(5)17,
32(5)19,
33(3)9
- minimize,
13(1)1,
16(4)1117,
17(2)366,
17(5)740,
20(6)1297,
21(4)703,
21(5)977,
22(3)490,
22(5)773,
28(5)908
- most,
4(1)21,
4(2)179,
4(4)650,
7(2)183,
7(4)560,
9(2)125,
9(2)164,
9(2)257,
13(1)1,
13(1)21,
13(1)52,
13(2)181,
14(2)127,
14(2)265,
15(5)771,
16(1)35,
16(3)524,
16(3)687,
16(4)1156,
16(4)1319,
16(5)1411,
16(5)1467,
17(4)561,
17(4)600,
17(5)777,
18(2)139,
18(4)477,
18(6)659,
18(6)683,
18(6)752,
19(1)7,
19(3)427,
19(4)557,
19(5)804,
20(1)1,
20(2)259,
20(4)869,
21(2)286,
21(2)324,
21(3)502,
22(1)129,
22(3)431,
22(3)506,
22(4)638,
22(5)816,
22(6)1002,
27(6)1147,
27(6)1344,
28(1)106,
28(4)715,
28(4)747,
29(2)13,
31(1)4,
31(5)17,
32(1)1,
32(3)9,
32(5)18,
33(1)3,
34(1)2
- much,
4(2)283,
7(2)183,
7(3)404,
13(1)21,
13(1)124,
14(2)147,
16(3)524,
16(5)1613,
17(1)157,
17(2)233,
17(5)691,
18(1)1,
18(3)300,
18(4)355,
18(4)477,
19(3)444,
20(5)917,
20(6)1265,
21(3)430,
23(2)105,
28(2)207,
28(5)908,
30(4)18,
33(1)3,
33(3)10
- multithreading,
31(1)1
- nested,
15(3)400,
16(3)954,
18(6)649,
18(6)683,
19(4)557,
21(6)1251,
31(6)23,
33(5)15
- net,
19(1)188,
20(5)917,
34(1)6
- off, trade-,
16(3)798,
16(5)1449,
20(6)1195,
21(5)1028,
30(1)4
- on-line,
16(5)1399,
20(1)208,
21(3)569,
31(6)20
- overhead,
9(2)164,
14(1)1,
14(1)28,
16(3)370,
16(4)1319,
16(5)1431,
17(4)635,
18(4)355,
18(6)659,
19(6)853,
20(3)586,
20(5)980,
20(6)1111,
20(6)1195,
20(6)1223,
20(6)1265,
21(2)324,
21(6)1251,
22(3)431,
22(5)932,
27(6)1049,
28(1)1,
28(1)70,
28(1)106,
28(1)134,
28(5)908,
30(4)22,
31(4)13,
31(5)17,
32(4)15,
32(5)17,
34(1)4
- parallelism,
6(2)159,
7(2)270,
7(2)348,
7(3)404,
7(4)501,
9(3)319,
9(4)491,
9(4)618,
10(4)579,
11(1)90,
11(4)562,
11(4)598,
12(2)203,
13(1)99,
14(1)28,
15(3)563,
15(5)771,
16(3)305,
16(3)524,
16(3)798,
16(4)1248,
16(6)1737,
17(2)233,
17(4)600,
18(3)268,
18(4)477,
19(6)853,
19(6)899,
19(6)1031,
20(3)635,
20(6)1131,
20(6)1195,
21(2)189,
21(2)240,
21(6)1251,
22(2)296,
27(6)1097,
28(5)942,
33(3)10,
34(1)3
- parallelize,
16(4)1248,
19(6)942,
20(6)1195
- parameter,
5(3)318,
9(2)164,
10(2)189,
14(2)265,
14(3)339,
14(4)471,
16(2)175,
16(5)1411,
17(4)561,
18(6)752,
19(1)188,
21(4)848,
27(6)1147,
31(3)10,
34(1)3
- practice,
14(4)490,
16(3)687,
16(3)872,
16(4)1117,
16(4)1319,
16(6)1768,
18(5)528,
19(3)413,
19(6)992,
20(1)51,
20(3)483,
20(3)635,
20(4)707,
20(4)768,
21(3)430,
22(4)701,
25(6)713,
30(4)18,
32(1)3,
32(6)21
- previous,
14(1)107,
14(4)490,
16(4)1097,
18(4)355,
18(4)454,
19(1)1,
19(4)617,
20(1)1,
20(4)845,
20(5)980,
20(6)1265,
21(1)1,
21(3)527,
21(5)977,
21(6)1196,
21(6)1251,
22(2)378,
22(4)701,
28(5)848,
29(1)2,
29(2)13,
30(6)32,
32(4)11,
32(4)13,
33(4)13,
34(1)1
- provably,
16(3)328,
16(3)607,
19(1)87,
21(2)240,
22(4)673,
22(4)701
- reduce,
4(2)149,
7(2)183,
9(3)408,
13(1)150,
14(1)28,
14(2)173,
14(2)265,
16(2)259,
16(3)428,
16(3)1051,
16(4)1319,
16(5)1512,
16(6)1768,
17(4)635,
17(5)691,
18(6)659,
19(6)1031,
20(2)302,
20(6)1111,
20(6)1223,
21(4)703,
22(2)378,
22(3)490,
22(5)932,
27(6)1097,
28(5)908,
28(5)942,
29(1)2,
30(3)17,
30(4)22,
30(5)27,
31(1)3,
31(3)9,
32(1)2,
32(4)11,
32(5)17
- require,
4(2)226,
4(4)601,
4(4)711,
4(4)758,
6(2)159,
9(2)235,
9(3)319,
9(3)408,
10(2)189,
14(4)574,
15(1)73,
16(1)3,
16(3)428,
16(3)939,
16(6)1768,
17(1)28,
17(1)85,
17(2)181,
17(2)394,
17(3)461,
17(4)600,
17(4)672,
18(1)30,
18(3)254,
18(6)730,
18(6)752,
19(4)557,
19(6)1031,
20(1)51,
20(3)635,
20(4)869,
20(6)1171,
20(6)1223,
21(1)90,
21(2)240,
21(4)703,
22(2)187,
22(2)224,
22(3)471,
22(4)638,
22(5)773,
28(1)1,
28(2)207,
28(3)476,
28(4)715,
30(4)18,
30(5)28,
31(5)17,
31(6)22,
32(1)3,
32(3)8,
32(4)12,
33(6)20
- required,
6(2)159,
6(4)527,
8(4)491,
9(2)198,
9(3)319,
12(4)643,
14(1)28,
14(3)396,
16(2)175,
16(3)986,
16(4)1156,
16(5)1399,
16(5)1449,
16(6)1768,
17(1)28,
17(5)691,
18(2)139,
18(4)477,
18(5)564,
19(6)942,
19(6)1053,
21(3)430,
22(3)540,
22(6)1037,
27(6)1097,
27(6)1147,
27(6)1270,
28(2)207,
28(3)517,
31(2)7,
33(3)9,
34(1)2
- requirement,
7(1)159,
8(4)577,
16(1)151,
18(1)30,
18(6)730,
19(6)899,
19(6)992,
20(1)116,
20(2)274,
20(6)1171,
28(5)848,
30(4)23,
30(6)33,
31(1)3,
32(3)9,
33(5)15,
34(1)5
- run-time,
4(2)239,
4(4)552,
8(4)419,
9(3)297,
9(3)367,
13(1)1,
13(2)269,
13(3)342,
14(1)1,
15(4)659,
16(1)151,
16(2)205,
16(3)577,
16(5)1449,
17(2)233,
18(4)355,
19(1)87,
19(1)188,
20(1)166,
20(6)1111,
20(6)1131,
20(6)1195,
21(1)1,
21(1)11,
21(2)324,
21(5)1028,
22(2)265,
22(2)296,
22(3)471,
22(3)490,
22(4)673,
22(5)932,
30(1)6,
30(2)8,
33(4)12
- running,
6(4)527,
14(2)265,
19(3)525,
19(4)557,
19(6)942,
20(1)166,
21(2)175,
22(4)673,
27(6)1097,
31(6)21
- runtime,
16(3)328,
19(3)525,
20(4)724,
21(2)240,
22(2)416,
22(4)673,
27(4)583,
29(1)2,
29(1)3,
29(2)13,
30(4)19,
30(4)22,
31(5)17,
31(6)23,
32(2)6,
32(3)9,
32(4)11,
32(4)13,
32(5)18,
33(6)21,
34(1)3
- scale,
4(1)1,
10(2)189,
30(4)22,
32(1)1,
32(3)9,
32(4)14,
33(1)5,
34(1)5
- schedule,
15(4)632,
16(4)1156,
17(5)740,
21(1)46,
22(5)773,
26(4)609,
29(6)34,
30(4)23,
34(1)1
- scheduler,
7(4)501,
17(5)740,
19(3)525,
20(6)1171,
29(6)33,
34(1)6
- scheduling,
1(1)142,
4(4)668,
4(4)678,
7(4)501,
11(1)57,
11(1)90,
11(3)404,
11(4)562,
11(4)585,
12(1)84,
12(2)203,
13(3)399,
14(3)299,
15(4)632,
16(3)649,
16(3)954,
16(4)1156,
17(5)740,
18(4)477,
19(3)525,
19(5)685,
19(6)853,
20(6)1195,
21(1)46,
22(2)296,
22(5)773,
29(6)33,
31(6)21,
32(3)9,
33(3)10
- serial,
20(3)483,
30(4)20,
33(4)14
- showing,
16(3)1051,
17(1)28,
17(1)85,
18(5)564,
19(1)188,
19(6)1053,
21(1)46,
21(3)569,
21(3)627,
21(5)914,
28(1)1,
28(3)476,
30(6)32,
31(4)14
- significantly,
7(1)159,
16(4)1156,
16(5)1431,
17(5)740,
18(4)355,
18(4)424,
18(6)752,
20(1)166,
20(5)917,
21(4)703,
21(5)977,
22(2)378,
28(5)908,
30(1)4,
30(4)20,
30(5)25,
30(6)31,
31(1)3,
31(3)9,
31(6)20,
33(6)21
- space,
1(2)287,
4(2)179,
9(2)164,
11(1)90,
13(1)1,
14(2)201,
15(5)876,
16(3)370,
16(4)1248,
16(4)1361,
17(1)123,
17(1)157,
17(4)635,
17(4)672,
17(5)777,
18(3)325,
18(4)477,
19(3)462,
19(6)992,
20(2)302,
20(2)344,
20(4)869,
20(6)1195,
20(6)1223,
21(4)813,
22(1)129,
22(2)296,
22(4)673,
24(4)409,
27(3)388,
28(2)290,
28(5)942,
29(1)2,
30(3)17,
30(5)28,
31(1)3,
31(2)8,
31(6)21,
32(4)11,
32(4)12,
32(4)13,
34(1)3
- Space-Efficient,
3(4)388
- support,
4(1)44,
4(2)226,
5(2)127,
5(3)381,
5(3)405,
7(4)501,
8(4)419,
8(4)577,
9(2)198,
9(2)235,
9(2)277,
9(3)319,
9(4)473,
12(2)178,
12(4)566,
13(1)52,
14(2)201,
16(3)305,
16(3)387,
16(4)1215,
16(5)1399,
16(5)1411,
16(5)1572,
17(2)394,
17(4)635,
18(1)16,
18(2)139,
18(4)401,
18(4)454,
19(1)153,
19(3)462,
19(3)492,
20(3)483,
20(4)869,
20(5)980,
20(5)1014,
20(6)1131,
20(6)1195,
21(2)324,
21(3)527,
21(6)1251,
22(2)187,
22(4)673,
22(4)701,
22(5)932,
22(6)1037,
28(2)207,
28(3)429,
28(3)517,
28(5)908,
30(2)8,
30(4)19,
30(4)20,
30(4)22,
31(3)9,
31(4)16,
31(5)17,
32(2)4,
32(2)6,
32(3)9,
32(4)11,
32(4)12,
32(5)17,
34(1)2,
34(1)4
- thread,
17(2)233,
17(4)600,
17(5)704,
21(2)240,
22(4)673,
27(6)1097,
28(5)942,
30(4)20,
31(5)17,
32(5)18
- time, Run-,
9(3)297,
13(1)1,
13(3)342,
14(1)1,
15(4)659,
16(3)577,
16(5)1449,
17(2)233,
18(4)355,
20(1)166,
20(6)1111,
20(6)1131,
20(6)1195,
21(1)11,
21(2)324,
22(2)265,
22(3)471,
22(3)490,
22(4)673,
30(1)6
- today,
19(1)188,
21(5)1028,
28(1)106,
32(3)9
- trade-off,
16(3)798,
16(5)1449,
20(6)1195,
21(5)1028,
30(1)4
- typically,
15(5)745,
16(4)1248,
18(1)30,
18(3)235,
18(4)424,
20(1)166,
20(2)302,
21(1)90,
21(2)370,
27(6)1049,
30(5)29,
32(4)13,
34(1)1,
34(1)2
- usage,
5(2)236,
9(2)125,
14(2)127,
17(5)691,
20(2)436,
21(4)790,
22(1)129,
22(3)540,
22(5)773,
23(2)105,
27(2)264,
30(2)8,
31(5)19,
31(6)21,
31(6)23,
32(2)4
- user,
4(1)1,
4(4)585,
4(4)711,
5(3)405,
5(4)513,
6(1)1,
7(2)183,
8(4)419,
8(4)524,
9(2)164,
9(2)277,
10(2)215,
12(2)143,
12(4)566,
14(1)54,
14(4)471,
16(3)387,
16(3)456,
16(3)727,
16(3)1024,
16(4)1248,
18(1)30,
19(1)153,
19(3)492,
20(4)869,
21(2)240,
21(4)790,
21(6)1077,
28(2)207,
28(3)517,
29(1)2,
32(2)4,
32(3)8
- value,
4(1)44,
4(2)226,
4(3)323,
4(4)527,
6(4)527,
7(3)426,
8(4)419,
8(4)577,
9(3)367,
9(3)408,
10(2)189,
13(2)181,
13(2)237,
13(2)269,
14(4)471,
15(5)876,
16(1)35,
16(3)387,
16(3)428,
16(4)1279,
16(5)1411,
16(5)1449,
16(6)1675,
17(1)63,
17(2)181,
17(2)394,
17(4)561,
18(3)254,
18(6)730,
20(2)302,
20(3)635,
20(4)724,
20(6)1111,
21(2)286,
22(2)340,
22(5)932,
22(6)1037,
28(3)389,
28(3)429,
30(4)18,
31(3)10,
31(3)12,
32(1)2,
32(3)7,
32(4)11,
32(4)15,
32(5)17,
32(6)23,
32(6)24,
33(5)16