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The Annals of Probability
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.
Steele, J. M. (1981). Subadditive Euclidean Functionals and Nonlinear Growth in Geometric Probability. The Annals of Probability, 9 (3), 365-376. http://dx.doi.org/10.1214/aop/1176994411
Date Posted: 27 November 2017
This document has been peer reviewed.