Exploiting Cardinality Encodings in Parallel Maximum Satisfiability

Cardinality constraints appear in many practical problems and have been well studied in the past. There are many CNF encodings for cardinality constraints, although it is not clear which encodings perform better. Indeed, different encodings can perform well over different problems. This paper examines a large number of cardinality encodings and evaluates their performance for solving the problem of Maximum Satisfiability (MaxSAT). Taking advantage of the diversification of cardinality encodings, we propose to exploit those encodings in parallel MaxSAT solving. Our parallel solver, pMAX, simultaneously searches in the lower and upper bound of the optimum value, and different cardinality encodings are used in each thread to increase the diversification of the search. Moreover, learned clauses are shared between threads during the search. Experimental results show that our parallel solver outperforms other sequential and parallel state-of-the-art MaxSAT solvers.