Algorithms for Counting 2-Sat Solutions and Colorings with Applications

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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( 1.246 n ) for formulas with n variables improves on the previous bound of O( 1.256 n ) by Dahllöf, Jonsson, and Wahlström. The algorithm uses only polynomial space. As a direct consequence we get an O(1.246 n ) time algorithm for counting maximum weighted independent sets in a graph.