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August, 1994 Rates of Convergence of Means for Distance-Minimizing Subadditive Euclidean Functionals
Kenneth S. Alexander
Ann. Appl. Probab. 4(3): 902-922 (August, 1994). DOI: 10.1214/aoap/1177004976

Abstract

Functionals L on finite subsets A of Rd are considered for which the value is the minimum total edge length among a class of graphs with vertex set equal to, or in some cases containing, A. Examples include minimal spanning trees, the traveling salesman problem, minimal matching and Steiner trees. Beardwood, Halton and Hammersley, and later Steele, have shown essentially that for {X1,,Xn} a uniform i.i.d. sample from [0,1]d,EL({X1,,Xn})/n(d1)/d converges to a finite constant. Here we bound the rate of this convergence, proving a conjecture of Beardwood, Halton and Hammersley.

Citation

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Kenneth S. Alexander. "Rates of Convergence of Means for Distance-Minimizing Subadditive Euclidean Functionals." Ann. Appl. Probab. 4 (3) 902 - 922, August, 1994. https://doi.org/10.1214/aoap/1177004976

Information

Published: August, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0809.60016
MathSciNet: MR1284990
Digital Object Identifier: 10.1214/aoap/1177004976

Subjects:
Primary: 60D05
Secondary: 05C80 , 90C27

Keywords: minimal matching , Minimal spanning tree , Steiner tree , subadditive Euclidean functional , Traveling salesman problem

Rights: Copyright © 1994 Institute of Mathematical Statistics

Vol.4 • No. 3 • August, 1994
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