TY - GEN
T1 - Approximation algorithms for MAX 4-SAT and rounding procedures for semidefinite programs
AU - Halperin, Eran
AU - Zwick, Uri
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1999.
PY - 1999
Y1 - 1999
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84948986297&partnerID=8YFLogxK
U2 - 10.1007/3-540-48777-8_16
DO - 10.1007/3-540-48777-8_16
M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???
AN - SCOPUS:84948986297
SN - 3540660194
SN - 9783540660194
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 202
EP - 217
BT - Integer Programming and Combinatorial Optimization - 7th International IPCO Conference, 1999, Proceedings
A2 - Cornuejols, Gerard
A2 - Burkard, Rainer E.
A2 - Woeginger, Gerhard J.
PB - Springer Verlag
T2 - 7th International Conference on Integer Programming and Combinatorial Optimization, IPCO 1999
Y2 - 9 June 1999 through 11 June 1999
ER -