Interactive Particle Systems on Hypergraphs, Drift Analysis and the WalkSAT algorithm

TL;DR

This paper studies the expected running time of the WalkSAT algorithm on satisfiable k-XOR SAT instances by introducing hypergraph-based particle systems and applying drift analysis, revealing dependence on hypergraph structure.

Contribution

It introduces hypergraph versions of particle systems and applies drift analysis to estimate WalkSAT's running time on satisfiable instances, linking it to hypergraph structural parameters.

Findings

Expected running time depends on the odd Cheeger drift of the hypergraph.

Hypergraph particle systems provide new tools for analyzing local search algorithms.

Reduction to drift analysis enables precise estimates of WalkSAT's performance.

Abstract

We analyze the expected running time of WalkSAT, a well-known local search procedure for satisfiability solving, on satisfiable instances of the k-XOR SAT problem. We obtain estimates of this expected running time by reducing the problem to a setting amenable to classical techniques from drift analysis. A crucial ingredient of this reduction is the definition of (new, explosive) hypergraph versions of interacting particle systems, notably of coalescing and annihilating random walks as well as the voter model. The use of these tools allows to show that the expected running time of WalkSAT depends on structural parameter (we call odd Cheeger drift) of the dual of the formula hypergraph.