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Acta Mathematica

, Volume 204, Issue 1, pp 91–150 | Cite as

The mean field traveling salesman and related problems

  • Johan WästlundEmail author
Article

Abstract

The edges of a complete graph on n vertices are assigned i.i.d. random costs from a distribution for which the interval [0, t] has probability asymptotic to t as t→0 through positive values. In this so called pseudo-dimension 1 mean field model, we study several optimization problems, of which the traveling salesman is the best known. We prove that, as n→∞, the cost of the minimum traveling salesman tour converges in probability to a certain number, approximately 2.0415, which is characterized analytically.

Mathematics Subject Classifications (2000)

Primary 60K35 90C35 

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Copyright information

© Institut Mittag-Leffler 2010

Authors and Affiliations

  1. 1.Department of Mathematical SciencesChalmers University of TechnologyGothenburgSweden

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