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Advances in Steiner Trees

  • Ding-Zhu Du
  • J. M. Smith
  • J. H. Rubinstein

Part of the Combinatorial Optimization book series (COOP, volume 6)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Jens Albrecht, Dietmar Cieslik
    Pages 1-13
  3. R. S. Booth, D. A. Thomas, J. F. Weng
    Pages 15-26
  4. Marcus Brazil, Doreen A. Thomas, Jia Feng Weng
    Pages 27-37
  5. Tao Jiang, Lusheng Wang
    Pages 39-62
  6. D. M. Warme, P. Winter, M. Zachariasen
    Pages 81-116
  7. Piotr Berman, Alexander Zelikovsky
    Pages 117-135
  8. Siu-Wing Cheng
    Pages 137-162
  9. Charles J. Colbourn, Guoliang Xue
    Pages 163-174
  10. A. S. C. Wade, V. J. Rayward-Smith
    Pages 255-281

About this book

Introduction

The Volume on Advances in Steiner Trees is divided into two sections. The first section of the book includes papers on the general geometric Steiner tree problem in the plane and higher dimensions. The second section of the book includes papers on the Steiner problem on graphs. The general geometric Steiner tree problem assumes that you have a given set of points in some d-dimensional space and you wish to connect the given points with the shortest network possible. The given set ofpoints are 3 Figure 1: Euclidean Steiner Problem in E usually referred to as terminals and the set ofpoints that may be added to reduce the overall length of the network are referred to as Steiner points. What makes the problem difficult is that we do not know a priori the location and cardinality ofthe number ofSteiner points. Thus)the problem on the Euclidean metric is not known to be in NP and has not been shown to be NP-Complete. It is thus a very difficult NP-Hard problem.

Keywords

Approximation algorithms complexity computer computer science graphs linear optimization network networks optimization

Editors and affiliations

  • Ding-Zhu Du
    • 1
  • J. M. Smith
    • 2
  • J. H. Rubinstein
    • 3
  1. 1.Department of Computer ScienceUniversity of MinnesotaUSA
  2. 2.Department of Mechanical & Industrial EngineeringUniversity of MassachusettsUSA
  3. 3.Department of MathematicsUniversity of MelbourneAustralia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-3171-2
  • Copyright Information Springer-Verlag US 2000
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-4824-3
  • Online ISBN 978-1-4757-3171-2
  • Series Print ISSN 1388-3011
  • Buy this book on publisher's site