Perturbed Message Passing for Constraint Satisfaction Problems

TL;DR

This paper introduces Perturbed Belief Propagation and Perturbed Survey Propagation, novel message passing algorithms that efficiently solve CSPs by directly producing solutions without decimation, outperforming existing methods in success rate and computational efficiency.

Contribution

The paper presents the first CSP solvers using stochastic perturbation of BP and SP, improving efficiency and success rates over traditional decimation methods.

Findings

Perturbed BP outperforms standard BP guided decimation in success rate and efficiency.

Perturbed SP surpasses SP-guided decimation in difficult CSP regimes.

The methods are effective on both random and real-world CSPs.

Abstract

We introduce an efficient message passing scheme for solving Constraint Satisfaction Problems (CSPs), which uses stochastic perturbation of Belief Propagation (BP) and Survey Propagation (SP) messages to bypass decimation and directly produce a single satisfying assignment. Our first CSP solver, called Perturbed Blief Propagation, smoothly interpolates two well-known inference procedures; it starts as BP and ends as a Gibbs sampler, which produces a single sample from the set of solutions. Moreover we apply a similar perturbation scheme to SP to produce another CSP solver, Perturbed Survey Propagation. Experimental results on random and real-world CSPs show that Perturbed BP is often more successful and at the same time tens to hundreds of times more efficient than standard BP guided decimation. Perturbed BP also compares favorably with state-of-the-art SP-guided decimation, which has a computational complexity that generally scales exponentially worse than our method (wrt the cardinality of variable domains and constraints). Furthermore, our experiments with random satisfiability and coloring problems demonstrate that Perturbed SP can outperform SP-guided decimation, making it the best incomplete random CSP-solver in difficult regimes.