Joseph E. Yukich (auth.)3540636668, 9783540636663
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 :
Introduction….Pages 1-8
Subadditivity and superadditivity….Pages 9-17
Subadditive and superadditive euclidean functionals….Pages 18-31
Asymptotics for euclidean functionals: The uniform case….Pages 32-52
Rates of convergence and heuristics….Pages 53-63
Isoperimetry and concentration inequalities….Pages 64-77
Umbrella theorems for euclidean functionals….Pages 78-96
Applications and examples….Pages 97-109
Minimal triangulations….Pages 110-125
Geometric location problems….Pages 126-130
Worst case growth rates….Pages 131-137 |
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