一种基于变量熵求解约束满足问题的置信传播算法

Abstract

Belief propagation (BP) is a powerful technique that has been applied to solve constraint satisfaction problems (CSPs). In this paper, for solving random CSPs with growing domains, we propose a new strategy based on the variable entropy to fix variables in the procedure of BP decimation. It has been proved that model RB, a representative random CSP with growing domains, exhibits an exact satisfiability phase transition phenomenon, and all instances of model RB are hard at the threshold. We perform the algorithm on the instances of model RB with two different groups of parameters. Numerical results show that the algorithm guided by BP can find solutions efficiently for instances in the regime that is close to the threshold. The running time of the algorithm grows exponentially with the problem size. Besides, the average freedom of the variables decreases as the control parameter (constraint tightness) increases.