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  • © 1998

Probability Theory of Classical Euclidean Optimization Problems

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1675)

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-X
  2. Introduction

    • Joseph E. Yukich
    Pages 1-8
  3. Subadditivity and superadditivity

    • Joseph E. Yukich
    Pages 9-17
  4. Rates of convergence and heuristics

    • Joseph E. Yukich
    Pages 53-63
  5. Isoperimetry and concentration inequalities

    • Joseph E. Yukich
    Pages 64-77
  6. Umbrella theorems for euclidean functionals

    • Joseph E. Yukich
    Pages 78-96
  7. Applications and examples

    • Joseph E. Yukich
    Pages 97-109
  8. Minimal triangulations

    • Joseph E. Yukich
    Pages 110-125
  9. Geometric location problems

    • Joseph E. Yukich
    Pages 126-130
  10. Worst case growth rates

    • Joseph E. Yukich
    Pages 131-137
  11. Back Matter

    Pages 138-152

About this book

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.

Keywords

  • Euclidean optimization
  • Median
  • Operations Research
  • Probability theory
  • combinatorial optimization
  • limit theorems
  • optimization
  • subadditivity

Bibliographic Information

  • Book Title: Probability Theory of Classical Euclidean Optimization Problems

  • Authors: Joseph E. Yukich

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0093472

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1998

  • Softcover ISBN: 978-3-540-63666-3Published: 18 March 1998

  • eBook ISBN: 978-3-540-69627-8Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 154

  • Topics: Geometry, Probability Theory

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions