Probability theory of classical Euclidean optimization problems / Joseph E. Yukich.

By: Yukich, Joseph
Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag): 1675.Publisher: Berlin ; New York : Springer, ©1998Description: 1 online resource (x, 152 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9783540696278; 354069627XSubject(s): Combinatorial probabilities | Stochastic geometry | Mathematical optimization | Random graphs | Probabilités combinatoires | Géométrie stochastique | Optimisation mathématique | Graphes aléatoires | Combinatorial probabilities | Mathematical optimization | Random graphs | Stochastic geometry | Limiettheorema's | Stochastische Geometrie | Zufallsgraph | Kombinatorische Wahrscheinlichkeitstheorie | Kombinatorische Optimierung | Analise combinatoriaGenre/Form: Electronic books. Additional physical formats: Print version:: Probability theory of classical Euclidean optimization problems.DDC classification: 510 s | 519.2 LOC classification: QA3 | L28 no. 1675Other classification: 31.70 Online resources: Click here to access online
Contents:
Introduction -- Subadditivity and Superadditivity -- Subadditive and Superaddititive 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 -- Geometrics Location Problems -- Worst Case Growth Rates -- Bibliography -- Index.
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.
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Includes bibliographical references (pages 138-148) and index.

Introduction -- Subadditivity and Superadditivity -- Subadditive and Superaddititive 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 -- Geometrics Location Problems -- Worst Case Growth Rates -- Bibliography -- Index.

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.

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