New Algorithms for Exact Satisfiability - Byskov, Jesper Makholm; Madsen, Bolette Ammitzbøll; Skjernaa, Bjarke (BRICS Report Series, 2003)
The Exact Satisfiability problem is to determine if a CNF-formula has a truth assignment satisfying exactly one literal in each clause; Exact 3-Satisfiability is the version in which each clause contains at most three literals. In this paper, we present algorithms for Exact Satisfiability and Exact 3-Satisfiability running in time O(2^0.2325n) and O(2^0.1379n), respectively. The previously best algorithms have running times O(2^0.2441n) for Exact Satisfiability (Monien, Speckenmeyer and Vornberger (1981)) and O(2^0.1626n) for Exact 3-Satisfiability (Kulikov and independently Porschen, Randerath and Speckenmeyer (2002)). We extend the case analyses of these papers and observe, that a formula not satisfying any of our cases has a small number of variables, for which we can try all possible truth assignments and for each such assignment solve the remaining part of the formula in polynomial time.