| Dewey Class |
516 |
| Title |
Probability Theory of Classical Euclidean Optimization Problems ([EBook] /) / by Joseph E. Yukich. |
| Author |
Yukich, Joseph E. |
| Other name(s) |
SpringerLink (Online service) |
| Publication |
Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 1998. |
| Physical Details |
X, 154 p. : online resource. |
| Series |
Lecture Notes in Mathematics 0075-8434 ; ; 1675 |
| ISBN |
9783540696278 |
| Summary Note |
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 note |
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. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) |
| Internet Site |
http://dx.doi.org/10.1007/BFb0093472 |
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