The Steiner Ratio

  • Dietmar Cieslik

Part of the Combinatorial Optimization book series (COOP, volume 10)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Dietmar Cieslik
    Pages 1-19
  3. Dietmar Cieslik
    Pages 21-58
  4. Dietmar Cieslik
    Pages 59-78
  5. Dietmar Cieslik
    Pages 79-98
  6. Dietmar Cieslik
    Pages 99-130
  7. Dietmar Cieslik
    Pages 131-139
  8. Dietmar Cieslik
    Pages 141-156
  9. Dietmar Cieslik
    Pages 157-169
  10. Dietmar Cieslik
    Pages 171-181
  11. Dietmar Cieslik
    Pages 183-195
  12. Dietmar Cieslik
    Pages 205-221
  13. Back Matter
    Pages 223-244

About this book

Introduction

Steiner's Problem concerns finding a shortest interconnecting network for a finite set of points in a metric space. A solution must be a tree, which is called a Steiner Minimal Tree (SMT), and may contain vertices different from the points which are to be connected. Steiner's Problem is one of the most famous combinatorial-geometrical problems, but unfortunately it is very difficult in terms of combinatorial structure as well as computational complexity. However, if only a Minimum Spanning Tree (MST) without additional vertices in the interconnecting network is sought, then it is simple to solve. So it is of interest to know what the error is if an MST is constructed instead of an SMT. The worst case for this ratio running over all finite sets is called the Steiner ratio of the space.
The book concentrates on investigating the Steiner ratio. The goal is to determine, or at least estimate, the Steiner ratio for many different metric spaces. The author shows that the description of the Steiner ratio contains many questions from geometry, optimization, and graph theory.
Audience: Researchers in network design, applied optimization, and design of algorithms.

Keywords

Finite Graph theory addition algorithms complexity geometry network networks optimization sets vertices

Authors and affiliations

  • Dietmar Cieslik
    • 1
  1. 1.Institute of Mathematics and C.S.University of GreifswaldGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-6798-8
  • Copyright Information Springer-Verlag US 2001
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-4856-4
  • Online ISBN 978-1-4757-6798-8
  • Series Print ISSN 1388-3011
  • About this book
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