Operations Research/Computer Science Interfaces Series

Graphs, Dioids and Semirings

New Models and Algorithms

Authors: Gondran, Michel, Minoux, Michel

  • A modern treatment of Graph Theory and its theoretical developments and recent algorithmic applications

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eBook $149.00
price for USA (gross)
  • ISBN 978-0-387-75450-5
  • Digitally watermarked, DRM-free
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  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-0-387-75449-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $189.00
price for USA
  • ISBN 978-1-4419-4529-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

The origins of Graph Theory date back to Euler (1736) with the solution of the celebrated 'Koenigsberg Bridges Problem'; and to Hamilton with the famous 'Trip around the World' game (1859), stating for the first time a problem which, in its most recent version – the 'Traveling Salesman Problem' -, is still the subject of active research. Yet, it has been during the last fifty years or so—with the rise of the electronic computers—that Graph theory has become an indispensable discipline in terms of the number and importance of its applications across the Applied Sciences. Graph theory has been especially central to Theoretical and Algorithmic Computer Science, and Automatic Control, Systems Optimization, Economy and Operations Research, Data Analysis in the Engineering Sciences. Close connections between graphs and algebraic structures have been widely used in the analysis and implementation of efficient algorithms for many problems, for example: transportation network optimization, telecommunication network optimization and planning, optimization in scheduling and production systems, etc.

The primary objectives of GRAPHS, DIOÏDS AND SEMIRINGS: New Models and Algorithms are to emphasize the deep relations existing between the semiring and dioïd structures with graphs and their combinatorial properties, while demonstrating the modeling and problem-solving capability and flexibility of these structures. In addition the book provides an extensive overview of the mathematical properties employed by "nonclassical" algebraic structures, which either extend usual algebra (i.e., semirings), or correspond to a new branch of algebra (i.e., dioïds), apart from the classical structures of groups, rings, and fields.

Reviews

From the reviews:

"The authors carefully explain with examples what is meant by a canonically ordered monoid, semiring and dioid, and go on to show in the book the relevance of these algebraic structures to such classic operations research problems related to graphs and networks … . recommend this as a book to be added in the libraries of institutions where graduate courses in OR are taught, because it may provide ideas for PhD students and others to explore further the concepts developed in this book … ." (R Bharath, Journal of the Operational Research Society, Vol. 60, 2009)


Table of contents (8 chapters)

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-0-387-75450-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-0-387-75449-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $189.00
price for USA
  • ISBN 978-1-4419-4529-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Graphs, Dioids and Semirings
Book Subtitle
New Models and Algorithms
Authors
Series Title
Operations Research/Computer Science Interfaces Series
Series Volume
41
Copyright
2008
Publisher
Springer US
Copyright Holder
Springer-Verlag US
eBook ISBN
978-0-387-75450-5
DOI
10.1007/978-0-387-75450-5
Hardcover ISBN
978-0-387-75449-9
Softcover ISBN
978-1-4419-4529-7
Series ISSN
1387-666X
Edition Number
1
Number of Pages
XX, 388
Number of Illustrations and Tables
26 b/w illustrations
Topics