Algorithms for (n,3)-MAXSAT and parameterization above the all-true assignment

Abstract

In this paper, we consider the (n,3)-MAXSAT problem. The problem is a special case of the Maximum Satisfiability problem with an additional requirement that in the input formula each variable appears at most three times. Here, we improve previous upper bounds for (n,3)-MAXSAT in terms of n (number of variables) and in terms of k (number of clauses that we are required to satisfy). Moreover, we prove that satisfying more clauses than the simple all true assignment is an NP-hard problem.