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  • © 1989

Concrete and Abstract Voronoi Diagrams

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Part of the book series: Lecture Notes in Computer Science (LNCS, volume 400)

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  • ISBN: 978-3-540-46874-5
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Table of contents (6 chapters)

  1. Front Matter

  2. Introduction

    Pages 3-7
  3. Acyclic partitions

    Pages 131-157
  4. Concluding remarks

    Pages 159-161
  5. Back Matter

About this book

The Voronoi diagram of a set of sites is a partition of the plane into regions, one to each site, such that the region of each site contains all points of the plane that are closer to this site than to the other ones. Such partitions are of great importance to computer science and many other fields. The challenge is to compute Voronoi diagrams quickly. The problem is that their structure depends on the notion of distance and the sort of site. In this book the author proposes a unifying approach by introducing abstract Voronoi diagrams. These are based on the concept of bisecting curves, which are required to have some simple properties that are actually possessed by most bisectors of concrete Voronoi diagrams. Abstract Voronoi diagrams can be computed efficiently and there exists a worst-case efficient algorithm of divide-and-conquer type that applies to all abstract Voronoi diagrams satisfying a certain constraint. The author shows that this constraint is fulfilled by the concrete diagrams based on large classes of metrics in the plane.

Keywords

  • Abstandsgeometrie
  • Algorithmen
  • Algorithms
  • Computer-Geometrie
  • Datenstruktur
  • Diagramm
  • algorithm
  • computer
  • computer science
  • data structures
  • algorithm analysis and problem complexity

Bibliographic Information

Buying options

eBook
USD 64.99
Price excludes VAT (USA)
  • ISBN: 978-3-540-46874-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 84.99
Price excludes VAT (USA)