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- Title
Efficient branch-and-bound algorithms for weighted MAX-2-SAT.
- Authors
Ibaraki, Toshihide; Imamichi, Takashi; Koga, Yuichi; Nagamochi, Hiroshi; Nonobe, Koji; Yagiura, Mutsunori
- 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.
- Subjects
ALGORITHMS; COMBINATORICS; MATHEMATICAL variables; ALGEBRA; MATHEMATICAL analysis; MATHEMATICS
- Publication
Mathematical Programming, 2011, Vol 127, Issue 2, p297
- ISSN
0025-5610
- Publication type
Article
- DOI
10.1007/s10107-009-0285-6