论文信息 - A Theoretical Framework of Hybrid Approaches to MAX SAT

A Theoretical Framework of Hybrid Approaches to MAX SAT

MAX SAT (the maximum satisfiability problem) is stated as follows: given a set of clauses with weights, find a truth assignment that maximizes the sum of the weights of the satisfied clauses. In this paper, we present a theoretical framewok of hybrid approaches combining the algorithms of Goemans-Williamson and Yannakakis. This framework leads to a unified analysis of the performance guarantees of proposed algorithms and also leads to a better approximation algorithm with performance guarantee 0.770, if we use a refinement of Yannakakis' algorithm.

[1] Uriel Feige,et al. Approximating the value of two power proof systems, with applications to MAX 2SAT and MAX DICUT , 1995, Proceedings Third Israel Symposium on the Theory of Computing and Systems.

[2] Mihalis Yannakakis,et al. On the approximation of maximum satisfiability , 1992, SODA '92.

[3] David P. Williamson,et al. New 3/4-Approximation Algorithms for the Maximum Satisfiability Problem , 1994, SIAM J. Discret. Math..

[4] David P. Williamson,et al. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming , 1995, JACM.

[5] Takao Asano,et al. Approximation algorithms for MAX SAT: Yannakakis vs. Goemans-Williamson , 1997, Proceedings of the Fifth Israeli Symposium on Theory of Computing and Systems.

[6] Takao Asano,et al. Approximation Algorithms for the Maximum Satisfiability Problem , 1996, Nord. J. Comput..