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.

Bibliographic Information

Book Title: Probability Theory of Classical Euclidean Optimization Problems
Authors: Joseph E. Yukich
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0093472
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1998
Softcover ISBN: 978-3-540-63666-3Published: 18 March 1998
eBook ISBN: 978-3-540-69627-8Published: 14 November 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: X, 154
Topics: Geometry, Probability Theory and Stochastic Processes

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Probability Theory of Classical Euclidean Optimization Problems

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