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The mean field traveling salesman and related problems

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Acta Mathematica

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.

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  1. Department of Mathematical Sciences, Chalmers University of Technology, SE-412 96, Gothenburg, Sweden

    Johan Wästlund

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  1. Johan Wästlund
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Wästlund, J. The mean field traveling salesman and related problems. Acta Math 204, 91–150 (2010). https://doi.org/10.1007/s11511-010-0046-7

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  • DOI: https://doi.org/10.1007/s11511-010-0046-7

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