An improved algorithm for the $$(n, 3)$$-MaxSAT problem: asking branchings to satisfy the clauses

Abstract

We study the $$(n, 3)$$ -MaxSAT problem where we are given an integer k and a CNF formula with n variables, each of which appears in at most 3 clauses, and the question is whether there is an assignment that satisfies at least k clauses. Based on refined observations, we propose a branching algorithm for the $$(n, 3)$$ -MaxSAT problem which significantly improves 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. 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.