Is SP BP?

TL;DR

This paper investigates the relationship between Survey Propagation and Belief Propagation in solving constraint satisfaction problems, showing that SP cannot always be reduced to BP and identifying conditions for such reduction.

Contribution

It demonstrates that SP is not always reducible from BP for general problems and introduces weighted Probabilistic Token Passing as a unifying framework.

Findings

SP may not be reducible from BP in general CSPs

Conditions for reducibility are established

Unified framework for SP algorithms via probabilistic interpretation

Abstract

The Survey Propagation (SP) algorithm for solving $k$-SAT problems has been shown recently as an instance of the Belief Propagation (BP) algorithm. In this paper, we show that for general constraint-satisfaction problems, SP may not be reducible from BP. We also establish the conditions under which such a reduction is possible. Along our development, we present a unification of the existing SP algorithms in terms of a probabilistically interpretable iterative procedure -- weighted Probabilistic Token Passing.