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We apply the objective method of Aldous to the problem of finding the minimum-cost edge cover of the complete graph with random independent and identically distributed edge costs. The limit, as the number of vertices goes to infinity, of the expected minimum cost for this problem is known via a combinatorial approach of Hessler and Wästlund. We provide a… (More)

We study combinatorial optimisation problems on graphs in the mean-field model, which assigns independent and identically distributed random weights to the edges of the graph. Specifically, we focus on two generalisations of minimum weight matching on graphs. The first problem of minimum cost edge cover finds application in a computational linguistics… (More)

J o u r n a l o f P r o b a b i l i t y Electron. Abstract In a complete bipartite graph with vertex sets of cardinalities n and n , assign random weights from exponential distribution with mean 1, independently to each edge. We show that, as n → ∞, with n = n/α for any fixed α > 1, the minimum weight of many-to-one matchings converges to a constant… (More)

For several combinatorial optimization problems over random structures, the theory of local weak convergence from probability and the cavity method from statistical physics can be used to deduce a recursive equation for the distribution of a quantity of interest. We show that there is a unique solution to such a recursive distributional equation (RDE) when… (More)

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