Some spin glass ideas applied to the clique problem

Details Some spin glass ideas applied to the clique problem Some spin glass ideas applied to the clique problem

2006-05-12

arxiv.org/abs/cond-mat/0605336v1

Physics

Condensed Matter

Statistical Mechanics

21 pages, latex file

Scientific paper

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.

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