New Upper Bounds for Maximum Satisfiability

Abstract

The (unweighted) Maximum Satisfiability problem (MaxSat) is: Given a Boolean formula in conjunctive normal form, find a truth assignment that satisfies the largest number of clauses. This paper describes exact algorithms that provide new upper bounds for MaxSat. We prove that MaxSat can be solved in time O(|F|·1.3803K), where |F| is the length of a formula F in conjunctive normal form and K is the number of clauses in F. We also prove the time bounds O(|F|·1.3995k), where k is the maximum number of satisfiable clauses, and O(1.1279|F|), for the same problem. For Max2Sat this implies a bound of O(1.2722K).