Combinatorial Optimization

Shortest Connectivity

An Introduction with Applications in Phylogeny

Authors: Cieslik, Dietmar

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About this book

The problem of "Shortest Connectivity" has a long and convoluted history: given a finite set of points in a metric space, search for a network that connects these points with the shortest possible length. This shortest network must be a tree and may contain vertices different from the points which are to be connected. Over the years more and more real-life problems are given, which use this problem or one of its relatives as an application, as a subproblem or a model.

This volume is an introduction to the theory of "Shortest Connectivity", as the core of the so-called "Geometric Network Design Problems", where the general problem can be stated as follows: given a configuration of vertices and/or edges, find a network which contains these objects, satisfies some predetermined requirements, and which minimizes a given objective function that depends on several distance measures. A new application of shortest connectivity is also discussed, namely to create trees which reflect the evolutionary history of "living entities".

The aim in this graduate level text is to outline the key mathematical concepts that underpin these important questions in applied mathematics. These concepts involve discrete mathematics (particularly graph theory), optimization, computer science, and several ideas in biology.

 

Reviews

From the reviews of the first edition:

"The aim of this graduate-level text is to summarize mathematical concepts concerned with problems of shortest connectivity, and to demonstrate important applications of the theory, in particular in biology. … The book contains extensive references and gives rise to many problems for further research. … Examples are discussed in the history of evolution, taxonomy, historical linguistics and others." (Günther Karigl, Zentralblatt MATH, Vol. 1086, 2006)


Table of contents (1 chapters)

Buy this book

eBook $119.00
price for USA (gross)
  • ISBN 978-0-387-23539-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.00
price for USA
  • ISBN 978-0-387-23538-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.00
price for USA
  • ISBN 978-1-4614-9853-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Shortest Connectivity
Book Subtitle
An Introduction with Applications in Phylogeny
Authors
Series Title
Combinatorial Optimization
Series Volume
17
Copyright
2005
Publisher
Springer US
Copyright Holder
Springer-Verlag US
eBook ISBN
978-0-387-23539-4
DOI
10.1007/b101778
Hardcover ISBN
978-0-387-23538-7
Softcover ISBN
978-1-4614-9853-7
Series ISSN
1388-3011
Edition Number
1
Number of Pages
IX, 268
Topics