Approximation algorithms for the maximum satisfiability problem

Authors:
Takao Asano;Takao Ono;Tomio Hirata
Affiliations:
Department of Information and System Engineering, Chuo University, Bunkyo-ku, Tokyo 112, Japan;School of Engineering, Nagoya University, Nagoya 464-01, Japan;School of Engineering, Nagoya University, Nagoya 464-01, Japan
Venue:
Nordic Journal of Computing
Year:
1996

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Abstract

The maximum satisfiability problem (MAX SAT) is the following: 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 approximation algorithms for MAX SAT, including a 0.76544-approximation algorithm. The previous best approximation algorithm for MAX SAT was proposed by Goemans-Williamson and has a performance guarantee of 0.7584. Our algorithms are based on semidefinite programming and the 0.75-approximation algorithms of Yannakakis and Goemans-Williamson.