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A new algorithm approach to the general Lovász local lemma with applications to scheduling and satisfiability problems (extended abstract)

Authors:

Artur Czumaj,

Christian ScheidelerAuthors Info & Claims

STOC '00: Proceedings of the thirty-second annual ACM symposium on Theory of computing

Pages 38 - 47

https://doi.org/10.1145/335305.335310

Published: 01 May 2000 Publication History

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References

[1]

N. Alon. A parallel algorithmic version of the local lemma. Random Structures and Algorithms, 2(4):367- 387, 1991.

Digital Library

Google Scholar

[2]

N. Alon, A. Bar-Noy, N. Linial, and D. Peleg. A lower bound for radio broadcast. Journal on Computer and System Science, 43(2):290-298, 1991.

Digital Library

Google Scholar

[3]

N. Alon, C. McDiarmid, and B. Reed. Acyclic coloring of graphs. Random Structures and Algorithms, 2(3):277-288, 1991.

Digital Library

Google Scholar

[4]

N. Alon, J. Spencer, and P. Erd6s. The Probabilistic Method. John Wiley &: Sons, New York, 1992.

Google Scholar

[5]

T. Asano, K. Hori, T. Ono, and T. Hirata. A theoretical framework of hybrid approaches to MAX SAT. In Proc. of the 8th Syrup. on Algorithms and Computation (ISAAC), pages 153-162, 1997.

Digital Library

Google Scholar

[6]

T. Asano and D. Williamson. Improved approximation algorithms for MAX SAT. In Proc. of the ilth A CM Syrup. on Discrete Algorithms (SODA), pages 96-105, 2000.

Digital Library

Google Scholar

[7]

J. Beck. An algorithmic approach to the Lov~isz local lemma. Random Structures and Algorithms, 2(4):343- 365, 1991.

Digital Library

Google Scholar

[8]

A. Z. Broder, A. M. Frieze, and E. Upfal. Static and dynamic path selection on expander graphs: A random walk approach. In Proc. of the 29th A CM Syrup. on Theory of Computing (STOC), pages 531-539, 1997.

Digital Library

Google Scholar

[9]

A. Czumaj and C. Scheideler. Coloring non-uniform hypergraphs: A new algorithmic approach to the general Lovasz local lemma. In Proc. of the 11th A CM Syrup. on Discrete Algorithms (SODA), pages 30-39, 2000.

Digital Library

Google Scholar

[10]

P. Erd6s and L. Lovisz. Problems and results on 3- chromatic hypergraphs and some related questions. In A. Hajnai, R. Rado, and V. S6s, editors, Infinite and Finite Sets (to Paul Erdds on his 60th birthday), pages 609-627. North-Holland, Amsterdam, 1975.

Google Scholar

[11]

P. Erd6s and J. Spencer. Lopsided Lovisz local lemma and latin transversals. Discrete Applied Mathematics, 30:151-154, 1991.

Digital Library

Google Scholar

[12]

U. Feige and C. Scheideler. Improved bounds for acyclic job shop scheduling. In Proc. of the 30th A CM Syrup. on Theory of Computing (STOC), pages 624-633, 1998.

Digital Library

Google Scholar

[13]

Z. Ffiredi and j. Kahn. On the dimensions of ordered sets of bounded degree. Order, 3:15-20, 1986.

Crossref

Google Scholar

[14]

M. Goemans and D. Williamson. New 3/4- approximation algorithms for the maximum satisfiability problem. SiAM Journal on Computing, 7:656-666, 1994.

Digital Library

Google Scholar

[15]

M. Goemans and D. Williamson. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. Journal of the ACM, 42:1115-1145, 1995.

Digital Library

Google Scholar

[16]

L. A. Goldberg, M. Paterson, A. Srinivasan, and E. Sweedyk. Better approximation guarantees for jobshop scheduling. In Proc. of the 8th A CM Syrup. on Discrete Algorithms (SODA), pages 599-608, 1997.

Digital Library

Google Scholar

[17]

H. Hind, M. Molloy, and B. Reed. Colouring a graph frugally. Combinatorica, 17(4):469-482, 1997.

Crossref

Google Scholar

[18]

D. Johnson. Approximation algorithms for combinatorial problems. Journal on Computer and System Science, 9:256-278, 1974.

Digital Library

Google Scholar

[19]

F. T. Leighton, B. M. Maggs, and S. B. Rao. Packet routing and job-shop scheduling in O(congestion + dilation) steps. Combinatorica, 14(2):167-186, 1994.

Crossref

Google Scholar

[20]

F. T. Leighton, B. M. Maggs, and A. W. Richa. Fast algorithms for finding o(congestion q- dilation) packet routing schedules. Technical report, CMU-CS-96-152, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, USA, 1996.

Google Scholar

[21]

T. Leighton, S. Rao, and A. Srinivasan. New algorithmic aspects of the Local Lemma with applications to routing and partitioning. In Proc. of the l Oth A CM Syrup. on Discrete Algorithms (SODA), pages 643-652, 1999.

Digital Library

Google Scholar

[22]

C.-J. Lu. A deterministic approximation algorithm for a minmax integer programming problem. In Proc. of the l Oth A CM Syrup. on Discrete Algorithms (SODA), pages 663-668, 1999.

Digital Library

Google Scholar

[23]

M. Molloy and B. Reed. Further algorithmic aspects of the local lemma. In Proc. of the 30th A CM Syrup. on Theory of Computing (STOC), pages 524-529, 1998.

Digital Library

Google Scholar

[24]

J. Radhakrishnan and A. Srinivasan. Improved bounds and algorithms for hypergraph two-coloring. In Proc. of the 39th IEEE Syrup. on Foundations of Computer Science (FOCS), pages 684-693, 1998.

Digital Library

Google Scholar

[25]

P. Raghavan and C. Thompson. Randomized rounding: A technique for provably good algorithms and algorithmic proofs. Combinatorica, 7:365-374, 1987.

Digital Library

Google Scholar

[26]

B. Reed. co, A, and X. Journal of Graph Theory, 27(4):177-212, 1998.

Digital Library

Google Scholar

[27]

J. Schmidt, A. Siegel, and A. Srinivasan. Chernoff- Hoeffding bounds for applications with limited independence. SIAM Journal on Discrete Mathematics, 8(2):223-250, 1995.

Digital Library

Google Scholar

[28]

D. Shmoys, C. Stein, and J. Wein. Improved approximation algorithms for shop scheduling problems. SIAM Journal on Computing, 23(3):617-632, 1994.

Digital Library

Google Scholar

[29]

J. Spencer. Probabilistic methods. In R. Graham, M. GrStschel, and L. Lovisz, editors, Handbook of Combinatorics, chapter 33. Elsevier Science, Amsterdam, 1995.

Digital Library

Google Scholar

[30]

A. Srinivasan. An extension of the Lovisz local lemma, and its applications to integer programming, in Proc. of the 7th A CM Syrup. on Discrete Algorithms (SODA), pages 6-15, 1996.

Digital Library

Google Scholar

[31]

M. Yannakakis. On the approximation of maximum satisfiability. Journal of Algorithms, 17:475-502, 1994.

Digital Library

Google Scholar

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Hu ZLi DZhang YGuo DLi Z(2019)Branch schedulingProceedings of the International Symposium on Quality of Service10.1145/3326285.3329071(1-10)Online publication date: 24-Jun-2019
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A new algorithm approach to the general Lovász local lemma with applications to scheduling and satisfiability problems (extended abstract)

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STOC '00: Proceedings of the thirty-second annual ACM symposium on Theory of computing

May 2000

756 pages

ISBN:1581131844

DOI:10.1145/335305

Chairmen:
Frances Yao,
Eugene Luks

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Published: 01 May 2000

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STOC00: The 32nd Annual ACM Symposium on Theory of Computing

May 21 - 23, 2000

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STOC '00 Paper Acceptance Rate 85 of 182 submissions, 47%;

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Hu ZLi DZhang YGuo DLi Z(2019)Branch schedulingProceedings of the International Symposium on Quality of Service10.1145/3326285.3329071(1-10)Online publication date: 24-Jun-2019
https://dl.acm.org/doi/10.1145/3326285.3329071
Hu ZTu JLi B(2019)Spear: Optimized Dependency-Aware Task Scheduling with Deep Reinforcement Learning2019 IEEE 39th International Conference on Distributed Computing Systems (ICDCS)10.1109/ICDCS.2019.00201(2037-2046)Online publication date: Jul-2019
https://doi.org/10.1109/ICDCS.2019.00201
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https://doi.org/10.1109/FOCS.2017.48
Grandl RKandula SRao SAkella AKulkarni JKeeton KRoscoe T(2016)GrapheneProceedings of the 12th USENIX conference on Operating Systems Design and Implementation10.5555/3026877.3026885(81-97)Online publication date: 2-Nov-2016
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Brandt SFischer OHirvonen JKeller BLempiäinen TRybicki JSuomela JUitto JWichs DMansour Y(2016)A lower bound for the distributed Lovász local lemmaProceedings of the forty-eighth annual ACM symposium on Theory of Computing10.1145/2897518.2897570(479-488)Online publication date: 19-Jun-2016
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Chung KPettie SSu HHalldórsson MDolev S(2014)Distributed algorithms for the Lovász local lemma and graph coloringProceedings of the 2014 ACM symposium on Principles of distributed computing10.1145/2611462.2611465(134-143)Online publication date: 15-Jul-2014
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Chandrasekaran KGoyal NHaeupler BCharikar M(2010)Deterministic algorithms for the Lovász Local LemmaProceedings of the twenty-first annual ACM-SIAM symposium on Discrete algorithms10.5555/1873601.1873681(992-1004)Online publication date: 17-Jan-2010
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Nagarajan VSviridenko M(2009)Tight Bounds for Permutation Flow Shop SchedulingMathematics of Operations Research10.1287/moor.1080.036834:2(417-427)Online publication date: 1-May-2009
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A constructive proof of the general lovász local lemma

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