Some spin glass ideas applied to the clique problem

TL;DR

This paper introduces a novel MCMC-based algorithm inspired by spin glass theory to address the NP-complete maximum clique problem, demonstrating promising performance on benchmark and random graphs.

Contribution

The paper presents a new algorithm combining spin glass ideas with MCMC for solving the maximum clique problem, with comparative analysis on benchmark graphs.

Findings

The new algorithm performs surprisingly well compared to standard methods.

It is applicable to both benchmark and random graphs.

The paper provides a clear explanation accessible to non-specialists.

Abstract

In this paper we introduce a new algorithm to study some NP-complete problems. This algorithm is a Markov Chain Monte Carlo (MCMC) inspired by the cavity method developed in the study of spin glass. We will focus on the maximum clique problem and we will compare this new algorithm with several standard algorithms on some DIMACS benchmark graphs and on random graphs. The performances of the new algorithm are quite surprising. Our effort in this paper is to be clear as well to those readers who are not in the field.