Optimal Interconnection Trees in the Plane

Theory, Algorithms and Applications

  • Marcus Brazil
  • Martin Zachariasen

Part of the Algorithms and Combinatorics book series (AC, volume 29)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Marcus Brazil, Martin Zachariasen
    Pages 1-82
  3. Marcus Brazil, Martin Zachariasen
    Pages 83-150
  4. Marcus Brazil, Martin Zachariasen
    Pages 151-218
  5. Marcus Brazil, Martin Zachariasen
    Pages 219-299
  6. Marcus Brazil, Martin Zachariasen
    Pages 301-317
  7. Back Matter
    Pages 319-344

About this book


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.


Network optimization Steiner trees algorithms combinatorics computational geometry

Authors and affiliations

  • Marcus Brazil
    • 1
  • Martin Zachariasen
    • 2
  1. 1.Melbourne School of EngineeringThe University of Melbourne Dept. of Electrical and Electronic EngineeringParkvilleAustralia
  2. 2.Dept. of Computer Science (DIKU)University of CopenhagenCopenhagenDenmark

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-13914-2
  • Online ISBN 978-3-319-13915-9
  • Series Print ISSN 0937-5511
  • Series Online ISSN 2197-6783
  • Buy this book on publisher's site