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We consider a multicommodity flow problem on a complete graph with the edges having random i.i.d capacities. We show that as the number of nodes tends to infinity, the maximum utility, given by the average of a concave function of each commodity flow, has an almost sure limit. Further, the asymptotically optimal flow uses only direct and two-hop paths, and… (More)

- Mustafa Khandwawala, Rajesh Sundaresan
- ArXiv
- 2012

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)

- Mustafa Khandwawala
- ArXiv
- 2014

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′ = dn/αe for any fixed α > 1, the minimum weight of many-to-one matchings converges to a constant (depending on α). Many-to-one matching arises as an… (More)

- Mustafa Khandwawala
- ArXiv
- 2014

Abstract: 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… (More)

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