Operations, Information and Decisions Papers

Document Type

Journal Article

Date of this Version

1981

Publication Source

Mathematics of Operations Research

Volume

6

Issue

6

Start Page

374

Last Page

378

DOI

10.1287/moor.6.3.374

Abstract

Let Xi, 1 ≤ i < ∞, be uniformly distributed in [0, 1]2 and let Tn be the length of the shortest closed path connecting {X1, X2, …, Xn}. It is proved that there is a constant 0 < β < ∞ such that for all ϵ > 0 ∑n=1∞p(|Tn/n−β‾‾‾‾‾√|>ϵ)<∞.n1∞pTnnβϵ∞

This result is essential in justifying Karp's algorithm for the traveling salesman problem under the independent model, and it settles a question posed by B. W. Weide.

Keywords

traveling salesman problem, complete convergence, sub additive processes, subadditive Euclidean functionals, jackknife, Efron-Stein inequality

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Date Posted: 27 November 2017