
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
Recommended Citation
Steele, J. M. (1981). Complete Convergence of Short Paths and Karp's Algorithm for the TSP. Mathematics of Operations Research, 6 (6), 374-378. http://dx.doi.org/10.1287/moor.6.3.374
Date Posted: 27 November 2017