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Improving exact algorithms for MAX-2-SAT

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Abstract

We study three new techniques that will speed up the branch-and-bound algorithm for the MAX-2-SAT problem: The first technique is a group of new lower bound functions for the algorithm and we show that these functions are admissible and consistently better than other known lower bound functions. The other two techniques are based on the strongly connected components of the implication graph of a 2CNF formula: One uses the graph to simplify the formula and the other uses the graph to design a new variable ordering. The experiments show that the simplification can reduce the size of the input substantially no matter what is the clause-to-variable ratio and that the new variable ordering performs much better when the clause-to-variable ratio is less than 2. A direct outcome of this research is a high-performance implementation of an exact algorithm for MAX-2-SAT which outperforms any implementation we know about in the same category. We also show that our implementation is a feasible and effective tool to solve large instances of the Max-Cut problem in graph theory.

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Correspondence to Haiou Shen.

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Preliminary results of this paper appeared in [20,21]. This research was supported in part by NSF under grant CCR-0098093.

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Shen, H., Zhang, H. Improving exact algorithms for MAX-2-SAT. Ann Math Artif Intell 44, 419–436 (2005). https://doi.org/10.1007/s10472-005-7036-z

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