Advertisement

Probability Theory of Classical Euclidean Optimization Problems

  • Authors
  • Joseph¬†E.¬†Yukich

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

Table of contents

  1. Front Matter
    Pages I-X
  2. Joseph E. Yukich
    Pages 1-8
  3. Joseph E. Yukich
    Pages 9-17
  4. Joseph E. Yukich
    Pages 53-63
  5. Joseph E. Yukich
    Pages 64-77
  6. Joseph E. Yukich
    Pages 78-96
  7. Joseph E. Yukich
    Pages 97-109
  8. Joseph E. Yukich
    Pages 110-125
  9. Joseph E. Yukich
    Pages 126-130
  10. Joseph E. Yukich
    Pages 131-137
  11. Back Matter
    Pages 138-152

About this book

Introduction

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

  • DOI https://doi.org/10.1007/BFb0093472
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-63666-3
  • Online ISBN 978-3-540-69627-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site