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Edge cover and poly...
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Hessler, MartinLinköpings universitet,Tillämpad matematik,Tekniska högskolan
(author)
Edge cover and polymatroid flow problems
- Article/chapterEnglish2010
Publisher, publication year, extent ...
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Institute of Mathematical Statistics,2010
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printrdacarrier
Numbers
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LIBRIS-ID:oai:DiVA.org:liu-65720
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https://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-65720URI
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https://research.chalmers.se/publication/137437URI
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https://gup.ub.gu.se/publication/137437URI
Supplementary language notes
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Language:English
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Summary in:English
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Subject category:ref swepub-contenttype
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Subject category:art swepub-publicationtype
Notes
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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.
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Wästlund, Johan,1971Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, matematik,Department of Mathematical Sciences, Mathematics,Chalmers(Swepub:cth)wastlund
(author)
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Linköpings universitetTillämpad matematik
(creator_code:org_t)
Related titles
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In:Electronic Journal of Probability: Institute of Mathematical Statistics15, s. 2200-22191083-6489
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