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New Trends in Discrete and Computational Geometry

  • Book
  • © 1993

Overview

Editors:
  1. János Pach

    1. Mathematical Institute of the Hungarian Academy of Sciences, Budapest, Hungary
      Courant Institute, New York University, New York, USA

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

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Table of contents (13 chapters)

  1. Front Matter

    Pages I-XI
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  2. Introduction

    • János Pach
    Pages 1-7

  3. Combinatorics and Algorithms of Arrangements

    • Leonidas Guibas, Micha Sharir
    Pages 9-36

  4. Backwards Analysis of Randomized Geometric Algorithms

    • Raimund Seidel
    Pages 37-67

  5. Epsilon-Nets and Computational Geometry

    • Jiří Matoušek
    Pages 69-89

  6. Complexity of Polytope Volume Computation

    • Leonid Khachiyan
    Pages 91-101

  7. Allowable Sequences and Order Types in Discrete and Computational Geometry

    • Jacob E. Goodman, Richard Pollack
    Pages 103-134

  8. Hyperplane Approximation and Related Topics

    • Nikolai M. Korneenko, Horst Martini
    Pages 135-161

  9. Geometric Transversal Theory

    • Jacob E. Goodman, Richard Pollack, Rephael Wenger
    Pages 163-198

  10. Hadwiger-Levi’s Covering Problem Revisited

    • Károly Bezdek
    Pages 199-233

  11. Geometric and Combinatorial Applications of Borsuk’s Theorem

    • Imre Bárány
    Pages 235-249

  12. A Survey of Recent Results in the Theory of Packing and Covering

    • Gábor Fejes Tóth, Wlodzimierz Kuperberg
    Pages 251-279

  13. Recent Developments in Combinatorial Geometry

    • W. Moser, J. Pach
    Pages 281-302

  14. Set Theoretic Constructions in Euclidean Spaces

    • Péter Komjáth
    Pages 303-325

  15. Back Matter

    Pages 327-340
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Keywords

About this book

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.

Editors and Affiliations

  • Mathematical Institute of the Hungarian Academy of Sciences, Budapest, Hungary

    János Pach

  • Courant Institute, New York University, New York, USA

    János Pach

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