Edge cover and polymatroid flow problems

Hessler, MartinLinköpings universitet,Tillämpad matematik,Tekniska högskolan (author)

In an n by n complete bipartite graph with independent exponentially distributed edge costs, we ask for the minimum total cost of a set of edges of which each vertex is incident to at least one. This so-called minimum edge cover problem is a relaxation of perfect matching. We show that the large n limit cost of the minimum edge cover is W(1)(2) + 2W(1) approximate to 1.456, where W is the Lambert W-function. In particular this means that the minimum edge cover is essentially cheaper than the minimum perfect matching, whose limit cost is pi(2)/6 approximate to 1.645. We obtain this result through a generalization of the perfect matching problem to a setting where we impose a (poly-)matroid structure on the two vertex-sets of the graph, and ask for an edge set of prescribed size connecting independent sets.

Wästlund, Johan,1971Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, matematik,Department of Mathematical Sciences, Mathematics,Chalmers(Swepub:cth)wastlund (author)
Linköpings universitetTillämpad matematik (creator_code:org_t)

In:Electronic Journal of Probability: Institute of Mathematical Statistics15, s. 2200-22191083-6489

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NATURAL SCIENCES: NATURAL SCIENCES; and Mathematics; and Probability Theo ...

By the university: Linköping University; Chalmers University of Technology; University of Gothenburg

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