Approximation algorithms for MAX 4-SAT and rounding procedures for semidefinite programs

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Abstract

Karloff and Zwick obtained recently an optimal 7/8-approximation algorithm for MAX 3-SAT. In an attempt to see whether similar methods can be used to obtain a 7/8-approximation algorithm for MAX SAT, we consider the most natural generalization of MAX 3-SAT, namely MAX 4-SAT. We present a semidefinite programming relaxation of MAX 4-SAT and a new family of rounding procedures that try to cope well with clauses of various sizes. We study the potential, and the limitations, of the relaxation and of the proposed family of rounding procedures using a combination of theoretical and experimental means. We select two rounding procedures from the proposed family of rounding procedures. Using the first rounding procedure we seem to obtain an almost optimal 0.8721-approximation algorithm for MAX 4-SAT. Using the second rounding procedure we seem to obtain an optimal 7/8-approximation algorithm for satisfiable instances of MAX 4-SAT. On the other hand, we show that no rounding procedure from the family considered can yield an approximation algorithm for MAX 4-SAT whose performance guarantee on all instances of the problem is greater than 0.8724. Although most of this paper deals specifically with the MAX 4-SAT problem, we believe that the new family of rounding procedures introduced, and the methodology used in the design and in the analysis of the various rounding procedures considered would have a much wider range of applicability.

Original languageEnglish
Title of host publicationInteger Programming and Combinatorial Optimization - 7th International IPCO Conference, 1999, Proceedings
EditorsGerard Cornuejols, Rainer E. Burkard, Gerhard J. Woeginger
PublisherSpringer Verlag
Pages202-217
Number of pages16
ISBN (Print)3540660194, 9783540660194
DOIs
StatePublished - 1999
Event7th International Conference on Integer Programming and Combinatorial Optimization, IPCO 1999 - Graz, Austria
Duration: 9 Jun 199911 Jun 1999

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1610
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference7th International Conference on Integer Programming and Combinatorial Optimization, IPCO 1999
Country/TerritoryAustria
CityGraz
Period9/06/9911/06/99

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