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.
Citation
Stefan Steinerberger. "New bounds for the traveling salesman constant." Adv. in Appl. Probab. 47 (1) 27 - 36, March 2015. https://doi.org/10.1239/aap/1427814579
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