Probability Theory of Classical Euclidean Optimization Problems

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Probability Theory of Classical Euclidean Optimization Problems is written by Joseph E. Yukich and published by Springer. It's available with International Standard Book Number or ISBN identification 354069627X (ISBN 10) and 9783540696278 (ISBN 13).

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.