Modulo Based CNF Encoding of Cardinality Constraints and Its Application to MaxSAT Solvers

Totalizer (TO) by Bailleux et al. and Half Sorting Network (HS) by Asin et al. are typical CNF encoding methods of cardinality constraint. The former is based on unary adder, while the latter is based on odd-even merge. Although TO is inferior to HS in terms of the number of clauses, TO is superior to HS in terms of the number of variables. We propose a new method called Modulo Totalizer (MTO) to overcome the disadvantage of TO. As an application, we have developed a partial MaxSAT solver with MTO. Preliminary experimental results show that our MTO based MaxSAT solver is comparable to or surpass the conventional TO based maxsat solvers.