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New Trends in Discrete and Computational Geometry

  • János Pach

Part of the Algorithms and Combinatorics book series (AC, volume 10)

Table of contents

  1. Front Matter
    Pages I-XI
  2. János Pach
    Pages 1-7
  3. Leonidas Guibas, Micha Sharir
    Pages 9-36
  4. Jiří Matoušek
    Pages 69-89
  5. Leonid Khachiyan
    Pages 91-101
  6. Jacob E. Goodman, Richard Pollack
    Pages 103-134
  7. Nikolai M. Korneenko, Horst Martini
    Pages 135-161
  8. Jacob E. Goodman, Richard Pollack, Rephael Wenger
    Pages 163-198
  9. Károly Bezdek
    Pages 199-233
  10. Gábor Fejes Tóth, Wlodzimierz Kuperberg
    Pages 251-279
  11. W. Moser, J. Pach
    Pages 281-302
  12. Péter Komjáth
    Pages 303-325
  13. Back Matter
    Pages 327-340

About this book

Introduction

Discrete and computational geometry are two fields which in recent years have benefitted from the interaction between mathematics and computer science. The results are applicable in areas such as motion planning, robotics, scene analysis, and computer aided design. The book consists of twelve chapters summarizing the most recent results and methods in discrete and computational geometry. All authors are well-known experts in these fields. They give concise and self-contained surveys of the most efficient combinatorical, probabilistic and topological methods that can be used to design effective geometric algorithms for the applications mentioned above. Most of the methods and results discussed in the book have not appeared in any previously published monograph. In particular, this book contains the first systematic treatment of epsilon-nets, geometric tranversal theory, partitions of Euclidean spaces and a general method for the analysis of randomized geometric algorithms. Apart from mathematicians working in discrete and computational geometry this book will also be of great use to computer scientists and engineers, who would like to learn about the most recent results.

Keywords

Algorithmentheorie Approximation von Hyperebenen Combinatorics Epsilonnetze Kombinatorik Konvexität Partition combinatorial geometry computational geometry discrete geometry diskrete Geometrie epsilon-nets mathematics robot robotics

Editors and affiliations

  • János Pach
    • 1
    • 2
  1. 1.Mathematical Institute of the Hungarian Academy of SciencesBudapestHungary
  2. 2.Courant InstituteNew York UniversityNew YorkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-58043-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-55713-5
  • Online ISBN 978-3-642-58043-7
  • Series Print ISSN 0937-5511
  • Buy this book on publisher's site
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