Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2007-011 (May 28, 2007)

Efficient Branch-and-Bound Algorithms for Weighted MAX-2-SAT
by Toshihide Ibaraki, Takashi Imamichi, Yuichi Koga, Hiroshi Nagamochi, Koji Nonobe, Mutsunori Yagiura

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MAX-2-SAT is one of the representative combinatorial problems and is known to be NP-hard. Given a set of $m$ clauses on $n$ propositional variables, where each clause contains at most two literals and is weighted by a positive real, MAX-2-SAT asks to find a truth assignment that maximizes the total weight of satisfied clauses. In this paper, we propose branch-and-bound exact algorithms for MAX-2-SAT utilizing three kinds of lower bounds. All lower bounds are based on a directed graph that represents conflicts among clauses, and two of them use a set covering representation of MAX-2-SAT. Computational comparisons on benchmark instances disclose that these algorithms are highly effective in reducing the number of search tree nodes as well as the computation time.