Algorithms for four variants of the exact satisfiability problem

Abstract

We present four polynomial space and exponential time algorithms for variants of the E XACT S ATISFIABILITY problem. First, an O(1.1120 n ) (where n is the number of variables) time algorithm for the NP-complete decision problem of E XACT 3-S ATISFIABILITY , and then an O(1.1907 n ) time algorithm for the general decision problem of E XACT S ATISFIABILITY . The best previous algorithms run in O(1.1193 n ) and O(1.2299 n ) time, respectively. For the #P-complete problem of counting the number of models for E XACT 3-S ATISFIABILITY we present an O(1.1487 n ) time algorithm. We also present an O(1.2190 n ) time algorithm for the general problem of counting the number of models for E XACT S ATISFIABILITY ; presenting a simple reduction, we show how this algorithm can be used for computing the permanent of a 0/1 matrix.