Probability Theory of Classical Euclidean Optimization Problems / Edition 1

by Joseph E. Yukich

Overview

This monograph describes the shastic 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.

Product Details

ISBN-13:	9783540636663
Publisher:	Springer Berlin Heidelberg
Publication date:	04/24/1998
Series:	Lecture Notes in Mathematics , #1675
Edition description:	1998
Pages:	154
Product dimensions:	6.10(w) x 9.25(h) x 0.01(d)

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.