Probability theory of classical Euclidean optimization problems
Author(s)
Bibliographic Information
Probability theory of classical Euclidean optimization problems
（Lecture notes in mathematics, 1675）
Springer, c1998
Available at / 91 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||1675RM980401
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC21:519.2/Y92070438330
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Note
Includes bibliographical references (p. [138]-148) and index
Description and Table of Contents
Description
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.
Table of Contents
Subadditivity and superadditivity.- Subadditive and superadditive euclidean functionals.- Asymptotics for euclidean functionals: The uniform case.- Rates of convergence and heuristics.- Isoperimetry and concentration inequalities.- Umbrella theorems for euclidean functionals.- Applications and examples.- Minimal triangulations.- Geometric location problems.- Worst case growth rates.
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