Probability Theory of Classical Euclidean Optimization Problems / by Joseph E. Yukich.

Format:

Book

Author/Creator:

Yukich, Joseph E., author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1675.

Lecture Notes in Mathematics, 0075-8434 ; 1675

Language:

English

Subjects (All):

Geometry.

Distribution (Probability theory).

Probability Theory and Stochastic Processes.

Local Subjects:

Geometry.

Probability Theory and Stochastic Processes.

Physical Description:

1 online resource (X, 154 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998.

System Details:

text file PDF

Summary:

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.

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.

Other Format:

Printed edition:

ISBN:

9783540696278

Access Restriction:

Restricted for use by site license.