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Every 2-CSP allows nontrivial approximation

Published: 22 May 2005 Publication History

Abstract

We use semidefinite programming to prove that any constraint satisfaction problem in two variables over any domain allows an efficient approximation algorithm that does provably better than picking a random assignment. To be more precise assume that each variable can take values in [d] and that each constraint rejects t out of the d2 possible input pairs. Then, for some universal constant c, we can, in probabilistic polynomial time, find an assignment whose objective value is, on expectation, within a factor (1- t/d2(1- c/d2 log d)) of optimal.

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Cited By

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  • (2023)Triplet Reconstruction and all other Phylogenetic CSPs are Approximation Resistant2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00024(253-284)Online publication date: 6-Nov-2023
  • (2009)Randomly supported independence and resistanceProceedings of the forty-first annual ACM symposium on Theory of computing10.1145/1536414.1536481(483-492)Online publication date: 31-May-2009
  • (2009)Every Permutation CSP of arity 3 is Approximation ResistantProceedings of the 2009 24th Annual IEEE Conference on Computational Complexity10.1109/CCC.2009.29(62-73)Online publication date: 15-Jul-2009
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    cover image ACM Conferences
    STOC '05: Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
    May 2005
    778 pages
    ISBN:1581139608
    DOI:10.1145/1060590
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    Publication History

    Published: 22 May 2005

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    Author Tags

    1. approximation algorithms
    2. constraint satisfaction
    3. semi-definite programming

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    STOC05: Symposium on Theory of Computing
    May 22 - 24, 2005
    MD, Baltimore, USA

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    Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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    Cited By

    View all
    • (2023)Triplet Reconstruction and all other Phylogenetic CSPs are Approximation Resistant2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00024(253-284)Online publication date: 6-Nov-2023
    • (2009)Randomly supported independence and resistanceProceedings of the forty-first annual ACM symposium on Theory of computing10.1145/1536414.1536481(483-492)Online publication date: 31-May-2009
    • (2009)Every Permutation CSP of arity 3 is Approximation ResistantProceedings of the 2009 24th Annual IEEE Conference on Computational Complexity10.1109/CCC.2009.29(62-73)Online publication date: 15-Jul-2009
    • (2008)The approximability of MAX CSP with fixed-value constraintsJournal of the ACM (JACM)10.1145/1391289.139129055:4(1-37)Online publication date: 18-Sep-2008
    • (2007)Sparse Random Linear Codes are Locally Decodable and TestableProceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science10.1109/FOCS.2007.65(590-600)Online publication date: 21-Oct-2007
    • (2007)On the Approximation Resistance of a Random PredicateProceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques10.1007/978-3-540-74208-1_11(149-163)Online publication date: 20-Aug-2007
    • (2005)Beating a random assignmentProceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques10.1007/11538462_12(134-145)Online publication date: 22-Aug-2005

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