Finite Energy Survey Propagation for Constraint Satisfaction Problems

Abstract

The Survey Propagation (SP) algorithm [1] has recently been shown to work well in the hard region for random K-SAT problems. SP has its origins in sophisticated arguments in statistical physics, and can be derived from an approach known as the cavity method, when applied at what is called the one-step replica symmetry breaking level. In its most general form, SP can be applied to general constraint satisfaction problems, and can also be used in the unsatisfiable region, where the aim is to minimize the number of violated constraints. In this paper, we formulate the SP-Y algorithm for general constraint satisfaction problems, applicable for minimizing the number of violated constraints. This could be useful, for example, in solving approximate subgraph isomorphism problems. Preliminary results show that SP can solve a few instances of induced subgraph isomorphism for which belief propagation failed to converge.