Probability Theory of Classical Euclidean Optimization Problems

• Main Author: Yukich, Joseph E. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998.
• Edition: 1st ed. 1998.
• Series: Lecture Notes in Mathematics, 1675
• Subjects: Geometry.; Probabilities.; Probability Theory and Stochastic Processes.

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 gr...

Table of 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.