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February, 1993 Probability and Problems in Euclidean Combinatorial Optimization
J. Michael Steele
Statist. Sci. 8(1): 48-56 (February, 1993). DOI: 10.1214/ss/1177011083


This article summarizes the current status of several streams of research that deal with the probability theory of problems of combinatorial optimization. There is a particular emphasis on functionals of finite point sets. The most famous example of such functionals is the length associated with the Euclidean traveling salesman problem (TSP), but closely related problems include the minimal spanning tree problem, minimal matching problems and others. Progress is also surveyed on (1) the approximation and determination of constants whose existence is known by subadditive methods, (2) the central limit problems for several functionals closely related to Euclidean functionals, and (3) analogies in the asymptotic behavior between worst-case and expected-case behavior of Euclidean problems. No attempt has been made in this survey to cover the many important applications of probability to linear programming, arrangement searching or other problems that focus on lines or planes.


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J. Michael Steele. "Probability and Problems in Euclidean Combinatorial Optimization." Statist. Sci. 8 (1) 48 - 56, February, 1993.


Published: February, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0768.90063
MathSciNet: MR1194443
Digital Object Identifier: 10.1214/ss/1177011083

Rights: Copyright © 1993 Institute of Mathematical Statistics


Vol.8 • No. 1 • February, 1993
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