Improved Algorithms for Maximum Satisfiability and Its Special Cases

The Maximum Satisfiability (MAXSAT) problem is an optimization version of the (SAT) in which one given a CNF formula with n variables and needs to find maximum number simultaneously satisfiable clauses. Recent works achieved significant progress proving new upper bounds on worst-case computational complexity MAXSAT. All these reduce general MAXSAT special case where each variable appears small times. So, it important design fast algorithms for (n,k)-MAXSAT construct efficient exact algorithm at most k times input formula. For (n,3)-MAXSAT problem, we O*(1.1749^n) improving previous record running time O*(1.191^n). (n,4)-MAXSAT O*(1.3803^n) best O*(1.4254^n). Using results, develop O*(1.0911^L) L length improves O*(1.0927^L) time.