Edge cover and polymatroid flow problems
Artikel i vetenskaplig tidskrift, 2010

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.

Random graphs

Combinatorial optimization

Författare

Martin Hessler

Johan Wästlund

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Electronic Journal of Probability

1083-6489 (ISSN)

Vol. 15 2200-2219

Ämneskategorier

Sannolikhetsteori och statistik