Algorithms and Combinatorics

Optimal Interconnection Trees in the Plane

Theory, Algorithms and Applications

Authors: Brazil, Marcus, Zachariasen, Martin

  • The first comprehensive book on the geometric Steiner tree problem since the 1990s
  • Clearly written proofs, supported by 120 color figures
  • Includes both the underlying mathematical theory and algorithms for Steiner trees, with an emphasis on exact solutions
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eBook 51,16 €
price for Spain (gross)
  • ISBN 978-3-319-13915-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 62,39 €
price for Spain (gross)
  • ISBN 978-3-319-13914-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 62,39 €
price for Spain (gross)
  • ISBN 978-3-319-35482-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

This book explores fundamental aspects of geometric network optimisation with applications to a variety of real world problems. It presents, for the first time in the literature, a cohesive mathematical framework within which the properties of such optimal interconnection networks can be understood across a wide range of metrics and cost functions. The book makes use of this mathematical theory to develop efficient algorithms for constructing such networks, with an emphasis on exact solutions.

Marcus Brazil and Martin Zachariasen focus principally on the geometric structure of optimal interconnection networks, also known as Steiner trees, in the plane. They show readers how an understanding of this structure can lead to practical exact algorithms for constructing such trees. 

The book also details numerous breakthroughs in this area over the past 20 years, features clearly written proofs, and is supported by 135 colour and 15 black and white figures. It will help graduate students, working mathematicians, engineers and computer scientists to understand the principles required for designing interconnection networks in the plane that are as cost efficient as possible.

About the authors

Marcus Brazil is Associate Professor and Reader at the Melbourne School of Engineering, The University of Melbourne, with a background in pure mathematics. He has worked on Steiner trees and network optimization problems for about 18 years, and has written more than 60 papers in this area, both on the theory of optimal network design and on industrial applications to Wireless Sensor Networks, Telecommunications, VLSI Physical Design, and Underground Mining Planning.

Martin Zachariasen is Head of Department and Professor at the Department of Computer Science, University of Copenhagen. He has worked on heuristics and exact methods for classical NP-hard problems, such as the geometric Steiner Tree Problem, as well as other optimization problems. His general research interests are in experimental algorithmics and computational combinatorial optimization, in particular related to VLSI design. As well as writing more than 40 papers on these topics, he is one of the developers of GeoSteiner, which is by far the most efficient software for solving a range of geometric Steiner tree problems.

Reviews

“The book presents an interesting and quickly developing area of research and will be useful for researchers working in this area and for those wanting to learn more about geometric Steiner tree problems.” (Yongtang Shi, Mathematical Reviews, December, 2015)

“The focus of this monograph is the geometric Steiner tree problem, i.e., how to optimally connect, in a geometric plane, a collection of n given terminals, together with an additional set of Steiner points, in terms of a measuring metric. … monograph is also intended as a textbook at a graduate level, thus comes with a decent collection of exercises, with varying difficulty degrees, at the end of each chapter, mostly assigned in a relevant context throughout the main text.” (Zhizhang Shen, zbMATH 1319.05044, 2015)


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Table of contents (5 chapters)

  • Euclidean and Minkowski Steiner Trees

    Brazil, Marcus (et al.)

    Pages 1-82

    Preview Buy Chapter 30,19 €
  • Fixed Orientation Steiner Trees

    Brazil, Marcus (et al.)

    Pages 83-150

    Preview Buy Chapter 30,19 €
  • Rectilinear Steiner Trees

    Brazil, Marcus (et al.)

    Pages 151-218

    Preview Buy Chapter 30,19 €
  • Steiner Trees with Other Cost Functions and Constraints

    Brazil, Marcus (et al.)

    Pages 219-299

    Preview Buy Chapter 30,19 €
  • Steiner Trees in Graphs and Hypergraphs

    Brazil, Marcus (et al.)

    Pages 301-317

    Preview Buy Chapter 30,19 €

Buy this book

eBook 51,16 €
price for Spain (gross)
  • ISBN 978-3-319-13915-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 62,39 €
price for Spain (gross)
  • ISBN 978-3-319-13914-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 62,39 €
price for Spain (gross)
  • ISBN 978-3-319-35482-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Optimal Interconnection Trees in the Plane
Book Subtitle
Theory, Algorithms and Applications
Authors
Series Title
Algorithms and Combinatorics
Series Volume
29
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-13915-9
DOI
10.1007/978-3-319-13915-9
Hardcover ISBN
978-3-319-13914-2
Softcover ISBN
978-3-319-35482-8
Series ISSN
0937-5511
Edition Number
1
Number of Pages
XVII, 344
Number of Illustrations and Tables
15 b/w illustrations, 135 illustrations in colour
Topics