Advances in Steiner Trees

1. Front Matter

   Pages i-xii

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2. The Steiner Ratio of finite-dimensional L _p -spaces

   • Jens Albrecht, Dietmar Cieslik

   Pages 1-13

3. Shortest Networks for One Line and Two Points in Space

   • R. S. Booth, D. A. Thomas, J. F. Weng

   Pages 15-26

4. Rectilinear Steiner Minimal Trees on Parallel Lines

   • Marcus Brazil, Doreen A. Thomas, Jia Feng Weng

   Pages 27-37

5. Computing Shortest Networks with Fixed Topologies

   • Tao Jiang, Lusheng Wang

   Pages 39-62

6. Steiner Trees, Coordinate Systems and NP-Hardness

   • J. F. Weng

   Pages 63-80

7. Exact Algorithms for Plane Steiner Tree Problems: A Computational Study

   • D. M. Warme, P. Winter, M. Zachariasen

   Pages 81-116

8. On Approximation of the Power-p and Bottleneck Steiner Trees

   • Piotr Berman, Alexander Zelikovsky

   Pages 117-135

9. Exact Steiner Trees in Graphs and Grid Graphs

   • Siu-Wing Cheng

   Pages 137-162

10. Grade of Service Steiner Trees in Series-Parallel Networks

    • Charles J. Colbourn, Guoliang Xue

    Pages 163-174

11. Preprocessing the Steiner Problem in Graphs

    • Cees Duin

    Pages 175-233

12. A Fully Polynomial Approximation Scheme for the Euclidean Steiner Augmentation Problem

    • J. Scott Provan

    Pages 235-253

13. Effective Local Search Techniques for the Steiner Tree Problem

    • A. S. C. Wade, V. J. Rayward-Smith

    Pages 255-281

14. Modern Heuristic Search Methods for the Steiner Tree Problem in Graphs

    • Stefan Voß

    Pages 283-323

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.

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

• Department of Computer Science, University of Minnesota, USA

  Ding-Zhu Du

• Department of Mechanical & Industrial Engineering, University of Massachusetts, USA

  J. M. Smith

• Department of Mathematics, University of Melbourne, Australia

  J. H. Rubinstein

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