A better algorithm for random k-SAT

TL;DR

This paper introduces a new polynomial-time algorithm that efficiently finds satisfying assignments for random k-SAT formulas at higher clause densities than previously possible, approaching the theoretical limit.

Contribution

The paper presents a novel algorithm that surpasses prior methods in solving random k-SAT problems at higher densities, nearing the theoretical threshold.

Findings

Algorithm finds solutions with high probability at m/n<(1-eps_k)2^k*ln(k)/k

Improves upon previous density bounds of 1.817*2^k/k

Achieves near-optimal performance for random k-SAT solving

Abstract

Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. We present a polynomial time algorithm that finds a satisfying assignment of F with high probability for constraint densities m/n<(1-eps_k)2^k\ln(k)/k, where eps_k->0. Previously no efficient algorithm was known to find solutions with non-vanishing probability beyond m/n=1.817.2^k/k [Frieze and Suen, J. of Algorithms 1996].