Skip to main content
SpringerLink
Log in
Book cover

The Steiner Ratio

  • Book
  • © 2001

Overview

Authors:
  1. Dietmar Cieslik

    1. Institute of Mathematics and C.S., University of Greifswald, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (12 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. The Historical Genesis

    • Dietmar Cieslik
    Pages 1-19

  3. Networks, Spaces and Algorithms

    • Dietmar Cieslik
    Pages 21-58

  4. Shortest Trees in Metric Spaces — A Survey

    • Dietmar Cieslik
    Pages 59-78

  5. The Steiner Ratio of Metric Spaces

    • Dietmar Cieslik
    Pages 79-98

  6. The Steiner Ratio of Banach-Minkowski Spaces

    • Dietmar Cieslik
    Pages 99-130

  7. Euclidean Spaces

    • Dietmar Cieslik
    Pages 131-139

  8. The Steiner Ratio of Neighboured Spaces

    • Dietmar Cieslik
    Pages 141-156

  9. Banach-Minkowski Planes

    • Dietmar Cieslik
    Pages 157-169

  10. The Steiner Ratio and the Embedding of Spaces

    • Dietmar Cieslik
    Pages 171-181

  11. The Steiner Ratio and Discrete Geometry

    • Dietmar Cieslik
    Pages 183-195

  12. The Dependence of the Steiner Ratio on the Dimension

    • Dietmar Cieslik
    Pages 197-203

  13. Related Questions

    • Dietmar Cieslik
    Pages 205-221

  14. Back Matter

    Pages 223-244
    Download chapter PDF
Back to top

Keywords

About this book

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.

Authors and Affiliations

  • Institute of Mathematics and C.S., University of Greifswald, Germany

    Dietmar Cieslik

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation