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

Auteur principal : Yukich, Joseph Elliott, 1956-, AuteurType de document : Livre numériqueCollection : Lecture notes in mathematics, 1675Langue : anglais.Éditeur : Berlin : Springer, 1998ISBN: 9783540636663.ISSN: 1617-9692.Sujet MSC : 60C05, Probability theory and stochastic processes, Combinatorial probability
60D05, Geometric probability and stochastic geometry
60F10, Limit theorems in probability theory, Large deviations
60F15, Limit theorems in probability theory, Strong limit theorems
60G55, Probability theory and stochastic processes, Point processes (e.g., Poisson, Cox, Hawkes processes)En-ligne : Springerlink | Zentralblatt | MathSciNet
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The monograph aims to develop the probability theory of solutions to the classical problems in Euclidean combinatorial optimization, computational geometry, and operations research. These problems are associated with graphs and the chief goal is to describe the almost sure behavior of the total edge lengths of these graphs.

The book consists of the following chapters: 1. Introduction. 2. Subadditivity and superadditivity. 3. Subadditive and superadditive Euclidean functionals. 4. Asymptotics for Euclidean functionals: The uniform case. 5. Rates of convergence and heuristics. 6. Isoperimetry and concentration inequalities. 7. Umbrella theorems for Euclidean functionals. 8. Applications and examples. 9. Minimal triangulations. 10. Geometric location problems. 11. Worst case growth rates. (Zentralblatt)

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