Exact MAX 2-SAT: Easier and faster

Martin Fürer, Shiva Prasad Kasiviswanathan

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

    4 Scopus citations

    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
    PublisherSpringer Verlag
    Pages272-283
    Number of pages12
    ISBN (Print)9783540695066
    DOIs
    StatePublished - 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

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

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