The Steiner Tree Problem

A Tour through Graphs, Algorithms, and Complexity

  • Hans Jürgen Prömel
  • Angelika Steger

Part of the Advanced Lectures in Mathematics book series (ALM)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Hans Jürgen Prömel, Angelika Steger
    Pages 1-22
  3. Hans Jürgen Prömel, Angelika Steger
    Pages 23-40
  4. Hans Jürgen Prömel, Angelika Steger
    Pages 41-62
  5. Hans Jürgen Prömel, Angelika Steger
    Pages 63-74
  6. Hans Jürgen Prömel, Angelika Steger
    Pages 75-86
  7. Hans Jürgen Prömel, Angelika Steger
    Pages 87-106
  8. Hans Jürgen Prömel, Angelika Steger
    Pages 107-132
  9. Hans Jürgen Prömel, Angelika Steger
    Pages 133-164
  10. Hans Jürgen Prömel, Angelika Steger
    Pages 165-190
  11. Hans Jürgen Prömel, Angelika Steger
    Pages 191-222
  12. Back Matter
    Pages 223-243

About this book

Introduction

In recent years, algorithmic graph theory has become increasingly important as a link between discrete mathematics and theoretical computer science. This textbook introduces students of mathematics and computer science to the interrelated fields of graphs theory, algorithms and complexity. No specific previous knowledge is assumed.
The central theme of the book is a geometrical problem dating back to Jakob Steiner. This problem, now called the Steiner problem, was initially of importance only within the context of land surveying. In the last decade, however, applications as diverse as VLSI-layout and the study of phylogenetic trees led to a rapid rise of interest in this problem. The resulting progress has uncovered fascinating connections between and within graph theory, the study of algorithms, and complexity theory. This single problem thus serves to bind and motivate these areas. The book's topics include: exact algorithms, computational complexity, approximation algorithms, the use of randomness, limits of approximability.
A special feature of the book is that each chapter ends with an "excursion" into some related area. These excursions reinforce the concepts and methods introduced for the Steiner problem by placing them in a broader context.


Keywords

Complexity Geometric Steiner Problems Graph Graph theory Graphs Terminal Sets algorithms

Authors and affiliations

  • Hans Jürgen Prömel
    • 1
  • Angelika Steger
    • 2
  1. 1.Institut für InformatikHumboldt Universität zu BerlinBerlinGermany
  2. 2.Institut für InformatikTechnische Universität MünchenMünchenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-322-80291-0
  • Copyright Information Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden 2002
  • Publisher Name Vieweg+Teubner Verlag
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-528-06762-5
  • Online ISBN 978-3-322-80291-0
  • Series Print ISSN 0932-7134
  • About this book