Junping Zhou

Junping Zhou, Huanyao Sun, Feifei Ma et al.

We introduce a diversified top-k partial MaxSAT problem, a combination of partial MaxSAT problem and enumeration problem. Given a partial MaxSAT formula F and a positive integer k, the diversified top-k partial MaxSAT is to find k maximal solutions for F such that the k maximal solutions satisfy the maximum number of soft clauses of F. This problem can be widely used in many applications including community detection, sensor place, motif discovery, and combinatorial testing. We prove the problem is NP-hard and propose an approach for solving the problem. The concrete idea of the approach is to design an encoding EE which reduces diversified top-k partial MaxSAT problem into partial MaxSAT problem, and then solve the resulting problem with state-of-art solvers. In addition, we present an algorithm MEMKC exactly solving the diversified top-k partial MaxSAT. Through several experiments we show that our approach can be successfully applied to the interesting problem.

Junping Zhou, Weihua Su, Minghao Yin

We propose a new approximate method for counting the number of the solutions for constraint satisfaction problem (CSP). The method derives from the partition function based on introducing the free energy and capturing the relationship of probabilities of variables and constraints, which requires the marginal probabilities. It firstly obtains the marginal probabilities using the belief propagation, and then computes the number of solutions according to the partition function. This allows us to directly plug the marginal probabilities into the partition function and efficiently count the number of solutions for CSP. The experimental results show that our method can solve both random problems and structural problems efficiently.