Approximation Algorithms for MAX 4-SAT and Rounding Procedures for Semidefinite Programs

@inproceedings{Halperin1999ApproximationAF,
  title={Approximation Algorithms for MAX 4-SAT and Rounding Procedures for Semidefinite Programs},
  author={Eran Halperin and Uri Zwick},
  booktitle={J. Algorithms},
  year={1999}
}
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… 

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