Random Instance Generation for MAX 3SAT

Abstract

MAX SAT is one of famous combinatorial optimization problems stated as follows: given a multiset of clauses, find an assignment that maximizes the number of satisfied clauses (that is equivalent to finding an assignment that minimizes the number of unsatisfied clauses). MAX 3SAT is restricted version of MAX SAT, that is, its input is restricted to a multiset of 3-clauses, i.e., each clause contains exactly 3 literals whose underlying variables are distinct each other. Since these problems are not only NP-hard problem, but MAX SNP-complete problem, there is no polynomial time approximation algorithm whose approximation ratio is close to 1 unless P = NP. Furthermore, Håstad showed that it is NP-hard to approximate MAX 3SAT within 8/7 - ε for any eε > 0 [5]. In spite of these negative results, many polynomial time approximation algorithms with proven approximation ratio for MAX SAT have been proposed [3,4,7].