Probability Theory of Classical Euclidean Optimization Problems (Lecture Notes in Mathematics, 1675)

Yukich, Joseph E.

ISBN 10: 3540636668 / ISBN 13: 9783540636663

Published by Springer, 1998

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Bibliographic Details

• Title: Probability Theory of Classical Euclidean Optimization Problems (Lecture Notes in Mathematics, 1675)
• Publisher: Springer
• Publication Date: 1998
• Language: English
• ISBN 10: 3540636668
• ISBN 13: 9783540636663
• Binding: Soft cover
• Condition: New

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Synopsis

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.