Steiner Trees in Industry

  • Xiu Zhen Cheng
  • Ding-Zhu Du

Part of the Combinatorial Optimization book series (COOP, volume 11)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Sunil Chopra, Chih-Yang Tsai
    Pages 175-201
  3. David Fernández-Baca
    Pages 203-234
  4. Clemens Gröpl, Stefan Hougardy, Till Nierhoff, Hans Jürgen Prömel
    Pages 235-279
  5. Thorsten Koch, Alexander Martin, Stefan Voß
    Pages 285-325
  6. Roman Novak, Joze Rugelj, Gorazd Kandus
    Pages 327-351
  7. Darko Skorin-Kapov
    Pages 353-375
  8. Doreen A. Thomas, Jia F. Weng
    Pages 405-426
  9. Martin Zachariasen
    Pages 467-507

About this book


This book is a collection of articles studying various Steiner tree prob­ lems with applications in industries, such as the design of electronic cir­ cuits, computer networking, telecommunication, and perfect phylogeny. The Steiner tree problem was initiated in the Euclidean plane. Given a set of points in the Euclidean plane, the shortest network interconnect­ ing the points in the set is called the Steiner minimum tree. The Steiner minimum tree may contain some vertices which are not the given points. Those vertices are called Steiner points while the given points are called terminals. The shortest network for three terminals was first studied by Fermat (1601-1665). Fermat proposed the problem of finding a point to minimize the total distance from it to three terminals in the Euclidean plane. The direct generalization is to find a point to minimize the total distance from it to n terminals, which is still called the Fermat problem today. The Steiner minimum tree problem is an indirect generalization. Schreiber in 1986 found that this generalization (i.e., the Steiner mini­ mum tree) was first proposed by Gauss.


algorithms Approximation communication computer computer network design interconnect layout metrics network neural networks phylogeny Routing telecommunications VLSI

Editors and affiliations

  • Xiu Zhen Cheng
    • 1
  • Ding-Zhu Du
    • 1
  1. 1.Department of Computer Science and EngineeringUniversity of MinnesotaMinneapolisUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag US 2001
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-7963-8
  • Online ISBN 978-1-4613-0255-1
  • Series Print ISSN 1388-3011
  • Buy this book on publisher's site