Interactive Particle Systems on Hypergraphs, Drift Analysis and the WalkSAT algorithm
Data Structures and Algorithms
2019-09-30 v1 Discrete Mathematics
Combinatorics
Probability
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.
Cite
@article{arxiv.1909.12353,
title = {Interactive Particle Systems on Hypergraphs, Drift Analysis and the WalkSAT algorithm},
author = {Gabriel Istrate and Cosmin Bonchis and Mircea Marin},
journal= {arXiv preprint arXiv:1909.12353},
year = {2019}
}