A Two-Phase Exact Algorithm for MAX-SAT and Weighted MAX-SAT Problems

We describe a two phase algorithm for MAX{SAT and weighted MAX{ SAT problems. In the rst phase, we use the GSAT heuristic to nd a good solution to the problem. In the second phase, we use an enumera-tion procedure based on the Davis{Putnam{Loveland algorithm, to nd a provably optimal solution. The rst heuristic stage improves the performance of the algorithm by obtaining an upper bound on the minimum number of unsatissed clauses that can be used in pruning branches of the search tree. We compare our algorithm with an integer programming branch and cut algorithm. Our implementation of the two phase algorithm is faster 1 than the integer programming approach on many problems. However, the integer programming approach is more eeective than the two phase algorithm on some classes of problems, including MAX{2{SAT problems.