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Edge cover and polymatroid flow problems

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Edge cover and polymatroid flow problems
2.	Creator	Author's name, affiliation, country	Martin Hessler; Linköping University; Sweden
2.	Creator	Author's name, affiliation, country	Johan Wästlund; Chalmers University of Technology; Sweden
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Random graphs; Combinatorial optimization
3.	Subject	Subject classification	60C05; 90C27; 90C35
4.	Description	Abstract	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 $W(1)^2+2W(1)\approx 1.456$, 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 $\pi^2/6\approx 1.645$. 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.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2010-12-18
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/846
10.	Identifier	Digital Object Identifier	10.1214/EJP.v15-846
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 15
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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