Algorithms for Counting 2-Sat Solutions and Colorings with Applications

Authors:
Martin Fürer;Shiva Prasad Kasiviswanathan
Affiliations:
Computer Science and Engineering, Pennsylvania State University,;Computer Science and Engineering, Pennsylvania State University,
Venue:
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Year:
2007

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Abstract

An algorithm is presented for exactly counting the number of maximum weight satisfying assignments of a 2-Cnfformula. The worst case running time of O( 1.246n) for formulas with nvariables 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.