Exact MAX 2-SAT: Easier and faster

Martin Fürer, Shiva Prasad Kasiviswanathan

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    3 Citations (Scopus)

    Abstract

    Prior algorithms known for exactly solving MAX 2-SAT improve upon the trivial upper bound only for very sparse instances. We present new algorithms for exactly solving (in fact, counting) weighted MAX 2-SAT instances. One of them has a good performance if the underlying constraint graph has a small separator decomposition, another has a slightly improved worst case performance. For a 2-SAT instance F with n variables, the worst case running time is Õ(21-1/(d̃(F)_1))n), where d̃(F) is the average degree in the constraint graph defined by F. We use strict α-gadgets introduced by Trevisan, Sorkin, Sudan, and Williamson to get the same upper bounds for problems like MAX 3-SAT and MAX CUT. We also introduce a notion of strict (α, β)-gadget to provide a framework that allows composition of gadgets. This framework allows us to obtain the same upper bounds for MAX k-SAT and MAX k-LIN-2.

    Original languageEnglish (US)
    Title of host publicationSOFSEM 2007
    Subtitle of host publicationTheory and Practice of Computer Science - 33rd Conference on Current Trends in Theory and Practice of Computer Science, Proceedings
    Pages272-283
    Number of pages12
    StatePublished - Dec 1 2007
    Event33rd Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2007 - Harrachov, Czech Republic
    Duration: Jan 20 2007Jan 26 2007

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume4362 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other33rd Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2007
    CountryCzech Republic
    CityHarrachov
    Period1/20/071/26/07

    Fingerprint

    Upper bound
    Separators
    Worst-case Performance
    Separator
    Graph in graph theory
    Decomposition
    Counting
    Trivial
    Chemical analysis
    Decompose
    Framework

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Fürer, M., & Kasiviswanathan, S. P. (2007). Exact MAX 2-SAT: Easier and faster. In SOFSEM 2007: Theory and Practice of Computer Science - 33rd Conference on Current Trends in Theory and Practice of Computer Science, Proceedings (pp. 272-283). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4362 LNCS).
    Fürer, Martin ; Kasiviswanathan, Shiva Prasad. / Exact MAX 2-SAT : Easier and faster. SOFSEM 2007: Theory and Practice of Computer Science - 33rd Conference on Current Trends in Theory and Practice of Computer Science, Proceedings. 2007. pp. 272-283 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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    abstract = "Prior algorithms known for exactly solving MAX 2-SAT improve upon the trivial upper bound only for very sparse instances. We present new algorithms for exactly solving (in fact, counting) weighted MAX 2-SAT instances. One of them has a good performance if the underlying constraint graph has a small separator decomposition, another has a slightly improved worst case performance. For a 2-SAT instance F with n variables, the worst case running time is {\~O}(21-1/(d̃(F)_1))n), where d̃(F) is the average degree in the constraint graph defined by F. We use strict α-gadgets introduced by Trevisan, Sorkin, Sudan, and Williamson to get the same upper bounds for problems like MAX 3-SAT and MAX CUT. We also introduce a notion of strict (α, β)-gadget to provide a framework that allows composition of gadgets. This framework allows us to obtain the same upper bounds for MAX k-SAT and MAX k-LIN-2.",
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    Fürer, M & Kasiviswanathan, SP 2007, Exact MAX 2-SAT: Easier and faster. in SOFSEM 2007: Theory and Practice of Computer Science - 33rd Conference on Current Trends in Theory and Practice of Computer Science, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4362 LNCS, pp. 272-283, 33rd Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2007, Harrachov, Czech Republic, 1/20/07.

    Exact MAX 2-SAT : Easier and faster. / Fürer, Martin; Kasiviswanathan, Shiva Prasad.

    SOFSEM 2007: Theory and Practice of Computer Science - 33rd Conference on Current Trends in Theory and Practice of Computer Science, Proceedings. 2007. p. 272-283 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4362 LNCS).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

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    Fürer M, Kasiviswanathan SP. Exact MAX 2-SAT: Easier and faster. In SOFSEM 2007: Theory and Practice of Computer Science - 33rd Conference on Current Trends in Theory and Practice of Computer Science, Proceedings. 2007. p. 272-283. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).