Solving Satisfiability using Decomposition and the Most Constrained Subproblem (Preliminary Report)

In this paper we provide SAT-solving procedures that use the idea of decomposition together with the heuristic of solving the most constrained subproblem first. We present two approaches. We provide an algorithm to find the most constrained subproblem of a propositional SAT problem in polynomial time. We use this algorithm iteratively to decompose a SAT problem into partitions. We also provide a polynomial-time algorithm that uses the idea of minimum vertex separators iteratively to provide different decompositions. We show how to solve SAT problems, using these algorithms to emphasize solving the most constrained subproblem first.