Advances in Applied Probability

New bounds for the traveling salesman constant

Stefan Steinerberger

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Abstract

Let X1, X2, . . . , Xn be independent and uniformly distributed random variables in the unit square [0, 1]2, and let L(X1, . . . , Xn) be the length of the shortest traveling salesman path through these points. In 1959, Beardwood, Halton and Hammersley proved the existence of a universal constant β such that limn→∞n -1/2L(X1, . . . , Xn) = β almost surely. The best bounds for β are still those originally established by Beardwood, Halton and Hammersley, namely 0.625 ≤ β ≤ 0.922. We slightly improve both upper and lower bounds.

Article information

Source
Adv. in Appl. Probab., Volume 47, Number 1 (2015), 27-36.

Dates
First available in Project Euclid: 31 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.aap/1427814579

Digital Object Identifier
doi:10.1239/aap/1427814579

Mathematical Reviews number (MathSciNet)
MR3327313

Zentralblatt MATH identifier
1309.60005

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 60F17: Functional limit theorems; invariance principles

Keywords
Traveling salesman constant Beardwood-Halton-Hammersley theorem

Citation

Steinerberger, Stefan. New bounds for the traveling salesman constant. Adv. in Appl. Probab. 47 (2015), no. 1, 27--36. doi:10.1239/aap/1427814579. https://projecteuclid.org/euclid.aap/1427814579


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