## A 7/8-Approximation Algorithm for MAX 3SAT? (1997)

Venue: | IN PROCEEDINGS OF THE 38TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE |

Citations: | 109 - 10 self |

### BibTeX

@INPROCEEDINGS{Karloff97a7/8-approximation,

author = {Howard Karloff and Uri Zwick},

title = {A 7/8-Approximation Algorithm for MAX 3SAT?},

booktitle = {IN PROCEEDINGS OF THE 38TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE},

year = {1997},

pages = {406--415},

publisher = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

We describe a randomized approximation algorithm which takes an instance of MAX 3SAT as input. If the instance---a collection of clauses each of length at most three---is satisfiable, then the expected weight of the assignment found is at least 7=8 of optimal. We provide strong evidence (but not a proof) that the algorithm performs equally well on arbitrary MAX 3SAT instances. Our algorithm uses semidefinite programming and may be seen as a sequel to the MAXCUT algorithm of Goemans and Williamson and the MAX 2SAT algorithm of Feige and Goemans. Though the algorithm itself is fairly simple, its analysis is quite complicated as it involves the computation of volumes of spherical tetrahedra. Hastad has recently shown that, assuming P 6= NP , no polynomial-time algorithm for MAX 3SAT can achieve a performance ratio exceeding 7=8, even when restricted to satisfiable instances of the problem. Our algorithm is therefore optimal in this sense. We also describe a method of obtaining direct semi...