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

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

14 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
Computer Science(all)

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)).

@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 F{\"u}rer and Kasiviswanathan, {Shiva Prasad}",

year = "2007",

doi = "10.1007/978-3-540-72870-2_5",

language = "English (US)",

isbn = "9783540728689",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "47--57",

booktitle = "Algorithmic Aspects in Information and Management - Third International Conference, AAIM 2007, Proceedings",

address = "Germany",

note = "3rd International Conference on Algorithmic Aspects in Information and Management, AAIM 2007 ; Conference date: 06-06-2007 Through 08-06-2007",

}

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

TY - GEN

T1 - Algorithms for counting 2-SAT solutions and colorings with applications

AU - Fürer, Martin

AU - Kasiviswanathan, Shiva Prasad

PY - 2007

Y1 - 2007

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.

UR - http://www.scopus.com/inward/record.url?scp=38149122178&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38149122178&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-72870-2_5

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

M3 - Conference contribution

AN - SCOPUS:38149122178

SN - 9783540728689

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 47

EP - 57

BT - Algorithmic Aspects in Information and Management - Third International Conference, AAIM 2007, Proceedings

PB - Springer Verlag

T2 - 3rd International Conference on Algorithmic Aspects in Information and Management, AAIM 2007

Y2 - 6 June 2007 through 8 June 2007

ER -

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)). https://doi.org/10.1007/978-3-540-72870-2_5

Algorithms for counting 2-SAT solutions and colorings with applications

Abstract

Publication series

Other

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this