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Efficient branch-and-bound algorithms for weighted MAX-2-SAT

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Abstract

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.

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Authors and Affiliations

  1. Department of Informatics, School of Science and Technology, Kwansei Gakuin University, 2-1 Gakuen, Sanda, 669-1337, Japan

    Toshihide Ibaraki

  2. Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Takashi Imamichi, Yuichi Koga & Hiroshi Nagamochi

  3. Department of Engineering and Design, Faculty of Engineering and Design, Hosei University, 2-17-1 Fujimi, Chiyoda, Tokyo, 102-8160, Japan

    Koji Nonobe

  4. Department of Computer Science and Mathematical Informatics, Graduate School of Information Science, Nagoya University, Furocho, Chikusaku, Nagoya, 464-8603, Japan

    Mutsunori Yagiura

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  1. Toshihide Ibaraki
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  2. Takashi Imamichi
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  4. Hiroshi Nagamochi
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Correspondence to Mutsunori Yagiura.

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Ibaraki, T., Imamichi, T., Koga, Y. et al. Efficient branch-and-bound algorithms for weighted MAX-2-SAT. Math. Program. 127, 297–343 (2011). https://doi.org/10.1007/s10107-009-0285-6

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