Algorithms for counting 2-SAT solutions and colorings with applications

Martin Furer, Shiva Prasad Kasiviswanathan

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

    11 Citations (Scopus)

    Abstract

    An algorithm is presented for exactly counting the number of maximum weight satisfying assignments of a 2-CNF formula. The worst case running time of O(1.246n) for formulas with n variables improves on the previous bound of O(1.256n) by Dahllöf, Jonsson, and Wahlström. The algorithm uses only polynomial space. As a direct consequence we get an O(1.246n) time algorithm for counting maximum weighted independent sets in a graph.

    Original languageEnglish (US)
    Title of host publicationAlgorithmic Aspects in Information and Management - Third International Conference, AAIM 2007, Proceedings
    Pages47-57
    Number of pages11
    StatePublished - Dec 1 2007
    Event3rd International Conference on Algorithmic Aspects in Information and Management, AAIM 2007 - Portland, OR, United States
    Duration: Jun 6 2007Jun 8 2007

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume4508 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other3rd International Conference on Algorithmic Aspects in Information and Management, AAIM 2007
    CountryUnited States
    CityPortland, OR
    Period6/6/076/8/07

    Fingerprint

    Coloring
    Colouring
    Counting
    Independent Set
    Assignment
    Polynomials
    Polynomial
    Graph in graph theory

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Furer, M., & Kasiviswanathan, S. P. (2007). Algorithms for counting 2-SAT solutions and colorings with applications. In Algorithmic Aspects in Information and Management - Third International Conference, AAIM 2007, Proceedings (pp. 47-57). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4508 LNCS).
    Furer, Martin ; Kasiviswanathan, Shiva Prasad. / Algorithms for counting 2-SAT solutions and colorings with applications. Algorithmic Aspects in Information and Management - Third International Conference, AAIM 2007, Proceedings. 2007. pp. 47-57 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
    @inproceedings{41704560d79c452dab1b949cb8aaf4af,
    title = "Algorithms for counting 2-SAT solutions and colorings with applications",
    abstract = "An algorithm is presented for exactly counting the number of maximum weight satisfying assignments of a 2-CNF formula. The worst case running time of O(1.246n) for formulas with n variables improves on the previous bound of O(1.256n) by Dahll{\"o}f, Jonsson, and Wahlstr{\"o}m. The algorithm uses only polynomial space. As a direct consequence we get an O(1.246n) time algorithm for counting maximum weighted independent sets in a graph.",
    author = "Martin Furer and Kasiviswanathan, {Shiva Prasad}",
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    Furer, M & Kasiviswanathan, SP 2007, Algorithms for counting 2-SAT solutions and colorings with applications. in Algorithmic Aspects in Information and Management - Third International Conference, AAIM 2007, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4508 LNCS, pp. 47-57, 3rd International Conference on Algorithmic Aspects in Information and Management, AAIM 2007, Portland, OR, United States, 6/6/07.

    Algorithms for counting 2-SAT solutions and colorings with applications. / Furer, Martin; Kasiviswanathan, Shiva Prasad.

    Algorithmic Aspects in Information and Management - Third International Conference, AAIM 2007, Proceedings. 2007. p. 47-57 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4508 LNCS).

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

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    AU - Kasiviswanathan, Shiva Prasad

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    N2 - An algorithm is presented for exactly counting the number of maximum weight satisfying assignments of a 2-CNF formula. The worst case running time of O(1.246n) for formulas with n variables improves on the previous bound of O(1.256n) by Dahllöf, Jonsson, and Wahlström. The algorithm uses only polynomial space. As a direct consequence we get an O(1.246n) time algorithm for counting maximum weighted independent sets in a graph.

    AB - An algorithm is presented for exactly counting the number of maximum weight satisfying assignments of a 2-CNF formula. The worst case running time of O(1.246n) for formulas with n variables improves on the previous bound of O(1.256n) by Dahllöf, Jonsson, and Wahlström. The algorithm uses only polynomial space. As a direct consequence we get an O(1.246n) time algorithm for counting maximum weighted independent sets in a graph.

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    Furer M, Kasiviswanathan SP. Algorithms for counting 2-SAT solutions and colorings with applications. In Algorithmic Aspects in Information and Management - Third International Conference, AAIM 2007, Proceedings. 2007. p. 47-57. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).