Statistical mechanics of optimization problems

Here I will present an introduction to the results that have been recently obtained in constraint optimization of random problems using statistical mechanics techniques. After presenting the general results, in order to simplify the presentation I will describe in details the problems related to the coloring of a random graph.Comment: proceedings of the conference SigmaPhi di Crete 2005, 10 pages, one figur

Random Walks with Long-Range Self-Repulsion on Proper Time

We introduce a model of self-repelling random walks where the short-range interaction between two elements of the chain decreases as a power of the difference in proper time. Analytic results on the exponent $\nu$ are obtained. They are in good agreement with Monte Carlo simulations in two dimensions. A numerical study of the scaling functions and of the efficiency of the algorithm is also presented.Comment: 25 pages latex, 4 postscript figures, uses epsf.sty (all included) IFUP-Th 13/92 and SNS 14/9