A rigorous proof of the cavity method for counting matchings

Details A rigorous proof of the cavity method for counting matchings A rigorous proof of the cavity method for counting matchings

2006-07-11

arxiv.org/abs/cond-mat/0607290v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

11 pages, 1 figure

Scientific paper

In this paper we rigorously prove the validity of the cavity method for the problem of counting the number of matchings in graphs with large girth. Cavity method is an important heuristic developed by statistical physicists that has lead to the development of faster distributed algorithms for problems in various combinatorial optimization problems. The validity of the approach has been supported mostly by numerical simulations. In this paper we prove the validity of cavity method for the problem of counting matchings using rigorous techniques. We hope that these rigorous approaches will finally help us establish the validity of the cavity method in general.

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