Abstract

We describe exact algorithms that provide new upper bounds for the Maximum Satisfiability problem (MaxSat). We prove that MaxSat can be solved in time O(|F | · 1.3972 K), 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 | · 1.3995 k), 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(1.2722 K). An exponential time approximation algorithm by Dantsin et al. uses an exact algorithm for MaxSat as a building block and is therefore also improved.

Citations