Open Access
June, 1981 Subadditive Euclidean Functionals and Nonlinear Growth in Geometric Probability
J. Michael Steele
Ann. Probab. 9(3): 365-376 (June, 1981). DOI: 10.1214/aop/1176994411


A limit theorem is established for a class of random processes (called here subadditive Euclidean functionals) which arise in problems of geometric probability. Particular examples include the length of shortest path through a random sample, the length of a rectilinear Steiner tree spanned by a sample, and the length of a minimal matching. Also, a uniform convergence theorem is proved which is needed in Karp's probabilistic algorithm for the traveling salesman problem.


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J. Michael Steele. "Subadditive Euclidean Functionals and Nonlinear Growth in Geometric Probability." Ann. Probab. 9 (3) 365 - 376, June, 1981.


Published: June, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0461.60029
MathSciNet: MR626571
Digital Object Identifier: 10.1214/aop/1176994411

Primary: 60D05
Secondary: 60C05 , 60F15 , 60G55

Keywords: Euclidean functional , Steiner tree , subadditive process , Traveling salesman problem

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 3 • June, 1981
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