Algorithms in Combinatorial Geometry

  • Herbert Edelsbrunner

Part of the EATCS Monographs in Theoretical Computer Science book series (EATCS, volume 10)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Combinatorial Geometry

    1. Front Matter
      Pages 1-1
    2. Herbert Edelsbrunner
      Pages 3-28
    3. Herbert Edelsbrunner
      Pages 29-44
    4. Herbert Edelsbrunner
      Pages 45-62
    5. Herbert Edelsbrunner
      Pages 63-82
    6. Herbert Edelsbrunner
      Pages 83-96
    7. Herbert Edelsbrunner
      Pages 97-118
  3. Fundamental Geometric Algorithms

    1. Front Matter
      Pages 121-121
    2. Herbert Edelsbrunner
      Pages 123-137
    3. Herbert Edelsbrunner
      Pages 139-176
    4. Herbert Edelsbrunner
      Pages 177-208
    5. Herbert Edelsbrunner
      Pages 209-239
    6. Herbert Edelsbrunner
      Pages 241-266
  4. Geometric and Algorithmic Applications

    1. Front Matter
      Pages 269-269
    2. Herbert Edelsbrunner
      Pages 271-291
    3. Herbert Edelsbrunner
      Pages 293-333
    4. Herbert Edelsbrunner
      Pages 335-357
    5. Herbert Edelsbrunner
      Pages 359-379
  5. Back Matter
    Pages 381-423

About this book

Introduction

Computational geometry as an area of research in its own right emerged in the early seventies of this century. Right from the beginning, it was obvious that strong connections of various kinds exist to questions studied in the considerably older field of combinatorial geometry. For example, the combinatorial structure of a geometric problem usually decides which algorithmic method solves the problem most efficiently. Furthermore, the analysis of an algorithm often requires a great deal of combinatorial knowledge. As it turns out, however, the connection between the two research areas commonly referred to as computa­ tional geometry and combinatorial geometry is not as lop-sided as it appears. Indeed, the interest in computational issues in geometry gives a new and con­ structive direction to the combinatorial study of geometry. It is the intention of this book to demonstrate that computational and com­ binatorial investigations in geometry are doomed to profit from each other. To reach this goal, I designed this book to consist of three parts, acorn binatorial part, a computational part, and one that presents applications of the results of the first two parts. The choice of the topics covered in this book was guided by my attempt to describe the most fundamental algorithms in computational geometry that have an interesting combinatorial structure. In this early stage geometric transforms played an important role as they reveal connections between seemingly unrelated problems and thus help to structure the field.

Keywords

Notation Permutation algorithm algorithms combinatorial geometry complexity geometry programming

Authors and affiliations

  • Herbert Edelsbrunner
    • 1
  1. 1.Dept. of Computer ScienceUniversity of Illinois at Urbana-ChampaignUrbanaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-61568-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 1987
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-64873-1
  • Online ISBN 978-3-642-61568-9
  • Series Print ISSN 1431-2654
  • About this book