Algorithms for counting 2-SAT solutions and colorings with applications

Martin Fürer; Shiva Prasad Kasiviswanathan

doi:10.1007/978-3-540-72870-2_5

Algorithms for counting 2-SAT solutions and colorings with applications

Martin Fürer, Shiva Prasad Kasiviswanathan

Eberly College of Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

22 Scopus citations

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 language	English (US)
Title of host publication	Algorithmic Aspects in Information and Management - Third International Conference, AAIM 2007, Proceedings
Publisher	Springer Verlag
Pages	47-57
Number of pages	11
ISBN (Print)	9783540728689
DOIs	https://doi.org/10.1007/978-3-540-72870-2_5
State	Published - 2007
Event	3rd International Conference on Algorithmic Aspects in Information and Management, AAIM 2007 - Portland, OR, United States Duration: Jun 6 2007 → Jun 8 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4508 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	3rd International Conference on Algorithmic Aspects in Information and Management, AAIM 2007
Country/Territory	United States
City	Portland, OR
Period	6/6/07 → 6/8/07

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-540-72870-2_5

Cite this

Fürer, 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). Springer Verlag. https://doi.org/10.1007/978-3-540-72870-2_5

Fürer, 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. Springer Verlag, 2007. pp. 47-57 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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.",

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Fürer, 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, Springer Verlag, pp. 47-57, 3rd International Conference on Algorithmic Aspects in Information and Management, AAIM 2007, Portland, OR, United States, 6/6/07. https://doi.org/10.1007/978-3-540-72870-2_5

Algorithms for counting 2-SAT solutions and colorings with applications. / Fürer, Martin; Kasiviswanathan, Shiva Prasad.
Algorithmic Aspects in Information and Management - Third International Conference, AAIM 2007, Proceedings. Springer Verlag, 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 proceeding › Conference contribution

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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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Fürer 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. Springer Verlag. 2007. p. 47-57. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-72870-2_5

Algorithms for counting 2-SAT solutions and colorings with applications

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