Combinatorial Optimization

Steiner Trees in Industry

Editors: Cheng, Xiuzhen, Du, Ding-Zhu (Eds.)

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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.

Table of contents (16 chapters)

  • Steiner Minimum Trees in Uniform Orientation Metrics

    Brazil, Marcus

    Pages 1-27

  • Genetic Algorithm Approaches to Solve Various Steiner Tree Problems

    Chakraborty, Goutam

    Pages 29-69

  • Neural Network Approaches to Solve Various Steiner Tree Problems

    Chakraborty, Goutam

    Pages 71-100

  • Steiner Tree Problems in VLSI Layout Designs

    Cho, Jun-Dong

    Pages 101-173

  • Polyhedral Approaches for the Steiner Tree Problem on Graphs

    Chopra, Sunil (et al.)

    Pages 175-201

Buy this book

eBook $269.00
price for USA (gross)
  • ISBN 978-1-4613-0255-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $349.00
price for USA
  • ISBN 978-1-4020-0099-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Steiner Trees in Industry
Editors
  • Xiuzhen Cheng
  • Ding-Zhu Du
Series Title
Combinatorial Optimization
Series Volume
11
Copyright
2001
Publisher
Springer US
Copyright Holder
Kluwer Academic Publishers
eBook ISBN
978-1-4613-0255-1
DOI
10.1007/978-1-4613-0255-1
Hardcover ISBN
978-1-4020-0099-7
Series ISSN
1388-3011
Edition Number
1
Number of Pages
XI, 507
Topics