Matchings on large diluted graphs : The cavity method at positive temperature.

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• Charles Bordenave, Université de Toulouse
• Monday 14 March 2011, 14:30-15:30
• MR12, Centre for Mathematical Sciences, Wilberforce Road, Cambridge.

If you have a question about this talk, please contact Elena Yudovina.

This talk pertains to rigorous derivations of the cavity method on large graphs. The focus of the present talk will be on the maximal matching problem but other combinatorial optimization problems will be mentioned.

We will obtain a limit theorem for the asymptotic size of a maximum matching of a graph sequence. When the graphs are random and converge in distribution to a unimodular Galton-Watson tree, the limiting quantity turns out to satisfy a recursive distributional equation, which we solve. This leads to an explicit formula that extends the well-known result by Karp and Sipser for Erdos-Renyi random graphs.

This is based on a joint work with Marc Lelarge and Justin Salez available at http://arxiv.org/abs/1102.0712

This talk is part of the Optimization and Incentives Seminar series.

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