Maximum 2-satisfiability (2004; Williams)
نویسنده
چکیده
In the maximum 2-satisfiability problem (abbreviated as Max 2-Sat), one is given a Boolean formula in conjunctive normal form, such that each clause contains at most two literals. The task is to find an assignment to the variables of the formula such that a maximum number of clauses is satisfied. Max 2-Sat is a classic optimization problem. Its decision version was proved NP-complete by Garey, Johnson, and Stockmeyer [7], in stark contrast with 2-Sat which is solvable in linear time [2]. To get a feeling for the difficulty of the problem, the NP-completeness reduction is sketched here. One can transform any 3-Sat instance F into a Max 2-Sat instance F , by replacing each clause of F such as
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