Some spin glass ideas applied to the clique problem
Antonio Iovanella · 2012
Be careful men Search every cook and nanny Uh, hook and granny Uh, crooked fan... uh, search everywhere! Doc (Snow White and the seven dwarfs, Walt Disney, 1937) 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.