Probability Theory of Classical Euclidean Optimization Problems: 1675 (Lecture Notes in Mathematics, 1675) - Softcover

Yukich, Joseph E.

Softcover

ISBN 10: 3540636668 ISBN 13: 9783540636663

Publisher: Springer, 1998

Synopsis

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.

About this title

Synopsis

This monograph on the probability theory of classical Euclidean optimization problems includes sections on subadditivity and superadditivity, asymptotics for Euclidean functionals, rates of convergence, heuristics, isoperimetry and concentration inequalities.

Edition details

• Publisher: Springer
• Publication date: 1998
• Language: English
• ISBN 10: 3540636668
• ISBN 13: 9783540636663
• Binding: Paperback
• Number of pages: 164