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Steiner Trees in Industry

  • Book
  • © 2001

Overview

Editors:
  1. Xiu Zhen Cheng

    1. Department of Computer Science and Engineering, University of Minnesota, Minneapolis, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Ding-Zhu Du

    1. Department of Computer Science and Engineering, University of Minnesota, Minneapolis, USA

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

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

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Table of contents (16 chapters)

  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
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Keywords

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.

Editors and Affiliations

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

    Xiu Zhen Cheng, Ding-Zhu Du

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