An Improved Branching Algorithm for (n, 3)-MaxSAT Based on Refined Observations

Abstract

In the MaxSAT problem, we are given a CNF formula (conjunctive normal form) and seek an assignment satisfying the maximum number of clauses. In the parameterized (n, 3)-MaxSAT problem we are given an integer k and a CNF formula such that each variable appears in at most 3 clauses, and are asked to find an assignment that satisfies at least k clauses. Based on refined observations, we propose a branching algorithm for the (n, 3)-MaxSAT problem with significant improvement over the previous results. More precisely, the running time of our algorithm can be bounded by \(O^*(1.175^k)\) and \(O^*(1.194^n)\), respectively, where n is the number of variables in the given CNF formula. Prior to our study, the running time of the best known exact algorithm can be bounded by \(O^*(1.194^k)\) and \(O^*(1.237^n)\), respectively.