A primal-dual approximation algorithm for Minsat

We characterize the optimal solution to the linear programming relaxation of the standard formulation for the minimum satisfiability problem. We give a O(nm(2)) combi-natorial algorithm to solve the fractional version of the minimum satisfiability problem optimally where n(m) is the number of variables (clauses). As a by-product, we obtain a 2(1 - 1/2(k)) approximation algorithm for the minimum satisfiability problem where k is the maximum number of literals in any clause. (c) 2021 Elsevier B.V. All rights reserved.