Analyzing Walksat on random formulas

TL;DR

This paper proves that the Walksat algorithm can find satisfying assignments for random k-SAT formulas in polynomial time under certain clause-to-variable ratios, improving previous theoretical bounds significantly.

Contribution

It provides a new, tighter analysis showing Walksat's polynomial-time performance on random formulas for a broader range of clause densities.

Findings

Walksat finds solutions in polynomial time when m/n< ho 2^k/k

Improves previous bounds by a factor of  ho k

Extends understanding of local search algorithms on random k-SAT

Abstract

Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. We prove that the Walksat algorithm from Papadimitriou (FOCS 1991)/Schoning (FOCS 1999) finds a satisfying assignment of F in polynomial time w.h.p. if m/n<\rho 2^k/k for a certain constant \rho>0. This is an improvement by a factor of $\Theta(k)$ over the best previous analysis of Walksat from Coja-Oghlan, Feige, Frieze, Krivelevich, Vilenchik (SODA 2009).