Acta Mathematica

The mean field traveling salesman and related problems

Johan Wästlund

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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.

Article information

Acta Math., Volume 204, Number 1 (2010), 91-150.

Received: 3 April 2008
Revised: 9 June 2009
First available in Project Euclid: 31 January 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 90C35: Programming involving graphs or networks [See also 90C27]

2010 © Institut Mittag-Leffler


Wästlund, Johan. The mean field traveling salesman and related problems. Acta Math. 204 (2010), no. 1, 91--150. doi:10.1007/s11511-010-0046-7.

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