Steiner Trees in Industry

1. Front Matter

   Pages i-xi

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2. Steiner Minimum Trees in Uniform Orientation Metrics

   • Marcus Brazil

   Pages 1-27

3. Genetic Algorithm Approaches to Solve Various Steiner Tree Problems

   • Goutam Chakraborty

   Pages 29-69

4. Neural Network Approaches to Solve Various Steiner Tree Problems

   • Goutam Chakraborty

   Pages 71-100

5. Steiner Tree Problems in VLSI Layout Designs

   • Jun-Dong Cho

   Pages 101-173

6. Polyhedral Approaches for the Steiner Tree Problem on Graphs

   • Sunil Chopra, Chih-Yang Tsai

   Pages 175-201

7. The Perfect Phylogeny Problem

   • David Fernández-Baca

   Pages 203-234

8. Approximation Algorithms for the Steiner Tree Problem in Graphs

   • Clemens Gröpl, Stefan Hougardy, Till Nierhoff, Hans Jürgen Prömel

   Pages 235-279

9. A Proposed Experiment on Soap Film Solutions of Planar Euclidean Steiner Trees

   • Frank K. Hwang

   Pages 281-283

10. SteinLib: An Updated Library on Steiner Tree Problems in Graphs

    • Thorsten Koch, Alexander Martin, Stefan Voß

    Pages 285-325

11. Steiner Tree Based Distributed Multicast Routing in Networks

    • Roman Novak, Joze Rugelj, Gorazd Kandus

    Pages 327-351

12. On Cost Allocation in Steiner Tree Networks

    • Darko Skorin-Kapov

    Pages 353-375

13. Steiner Trees and the Dynamic Quadratic Assignment Problem

    • Jim MacGregor Smith

    Pages 377-403

14. Polynomial Time Algorithms for the Rectilinear Steiner Tree Problem

    • Doreen A. Thomas, Jia F. Weng

    Pages 405-426

15. Minimum Networks for Separating and Surrounding Objects

    • Jia F. Weng

    Pages 427-439

16. A First Level Scatter Search Implementation for Solving the Steiner Ring Problem in Telecommunications Network Design

    • Jie Feng Xu, Steve Chiu, Fred Glover

    Pages 441-466

17. The Rectilinear Steiner Tree Problem: A Tutorial

    • Martin Zachariasen

    Pages 467-507

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

• Department of Computer Science and Engineering, University of Minnesota, Minneapolis, USA

  Xiu Zhen Cheng, Ding-Zhu Du

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