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In this paper we introduce a new algorithm to study some NP-completeproblems. This algorithm is a Markov Chain Monte Carlo (MCMC) inspired by thecavity method developed in the study of spin glass. We will focus on themaximum clique problem and we will compare this new algorithm with severalstandard algorithms on some DIMACS benchmark graphs and on random graphs. Theperformances of the new algorithm are quite surprising. Our effort in thispaper is to be clear as well to those readers who are not in the field.Comment: 21 pages, latex fil

Some Spin Glass Ideas Applied to the Clique Problem