Lecture Notes in Mathematics

By: Joseph E. Yukich

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Paperback | 18 March 1998 | Edition Number 7000

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164 Pages

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23.5 x 15.88 x 1.27

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This monograph describes the stochastic behavior of the solutions to the classic problems of Euclidean combinatorial optimization, computational geometry, and operations research. Using two-sided additivity and isoperimetry, it formulates general methods describing the total edge length of random graphs in Euclidean space. The approach furnishes strong laws of large numbers, large deviations, and rates of convergence for solutions to the random versions of various classic optimization problems, including the traveling salesman, minimal spanning tree, minimal matching, minimal triangulation, two-factor, and k-median problems. Essentially self-contained, this monograph may be read by probabilists, combinatorialists, graph theorists, and theoretical computer scientists.

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You Can Find This Book In

Non-Fiction Science Physics Mathematical Physics Business & Management Operational Research Mathematics Optimisation Probability & Statistics Geometry Euclidean Geometry Applied Mathematics

Stochastics

Introduction	p. 1
Subadditivity and Superadditivity	p. 9
Subadditive and Superadditive Euclidean Functionals	p. 18
Asymptotics for Euclidean Functionals: The Uniform Case	p. 32
Rates of Convergence and Heuristics	p. 53
Isoperimetry and Concentration Inequalities	p. 64
Umbrella Theorems for Euclidean Functionals	p. 78
Applications and Examples	p. 97
Minimal Triangulations	p. 110
Geometric Location Problems	p. 126
Worst Case Growth Rates	p. 131
Bibliography	p. 138
Index	p. 149
Table of Contents provided by Blackwell. All Rights Reserved.

Lecture Notes in Mathematics

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