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Algorithms and Combinatorics

Geometry of Cuts and Metrics

Authors: Deza, Michel Marie, Laurent, Monique

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eBook $119.00
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  • ISBN 978-3-642-04295-9
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  • Immediate eBook download after purchase
Hardcover $229.00
price for USA
  • ISBN 978-3-540-61611-5
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  • Usually dispatched within 3 to 5 business days.
Softcover $159.00
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  • ISBN 978-3-642-04294-2
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About this book

Cuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, distance geometry, combinatorial matrix theory, statistical physics, VLSI design etc. A main feature of this book is its interdisciplinarity. The book contains a wealth of results, from different mathematical disciplines, which are presented here in a unified and comprehensive manner. Geometric representations and methods turn out to be the linking theme. This book will provide a unique and invaluable source for researchers and graduate students.

From the Reviews:

"This book is definitely a milestone in the literature of integer programming and combinatorial optimization. It draws from the interdisciplinarity of these fields as it gathers methods and results from polytope theory, geometry of numbers, probability theory, design and graph theory around two objects, cuts and metrics. [… ] The book is very nicely written [… ] The book is also very well structured. With knowledge about the relevant terms, one can enjoy special subsections without being entirely familiar with the rest of the chapter. This makes it not only an interesting research book but even a dictionary. […  ] In my opinion, the book is a beautiful piece of work. The longer one works with it, the more beautiful it becomes." Robert Weismantel, Optima 56 (1997)

"… In short, this is a very interesting book which is nice to have." Alexander I. Barvinok, MR 1460488 (98g:52001)

"… This is a large and fascinating book. As befits a book which contains material relevant to so many areas of mathematics (and related disciplines such as statistics, physics, computing science, and economics), it is self-contained and written in a readable style. Moreover, the index, bibliography, and table of contents are all that they should be in such a work; it is easy to find as much or as little introductory material as needed." R.Dawson, Zentralblatt MATH Database 0885.52001

Reviews

From the reviews:

"This book is definitely a milestone in the literature of integer programming and combinatorial optimization. It draws from the Interdisciplinarity of these fields as it gathers methods and results from polytope theory, geometry of numbers, probability theory, design and graph theory around two objects, cuts and metrics. [… ] The book is very nicely written [… ] The book is also very well structured. With knowledge about the relevant terms, one can enjoy special subsections without being entirely familiar with the rest of the chapter. This makes it not only an interesting research book but even a dictionary. [… ] In my opinion, the book is a beautiful piece of work. The longer one works with it, the more beautiful it becomes." Robert Weismantel, Optima 56 (1997)

"… In short, this is a very interesting book which is nice to have." Alexander I. Barvinok, MR 1460488 (98g:52001)

"… This is a large and fascinating book. As befits a book which contains material relevant to so many areas of mathematics (and related disciplines such as statistics, physics, computing science, and economics), it is self-contained and written in a readable style. Moreover, the index, bibliography, and table of contents are all that they should be in such a work; it is easy to find as much or as little introductory material as needed." R.Dawson, Zentralblatt MATH Database 0885.52001

"This is a large and fascinating book. As befits a book which contains material relevant to so many areas of mathematics (and related disciplines such as statistics, physics, computing science, and economics), it is self-contained and written in a readable style. Moreover, the index, bibliography, and table of contents are all that they should be in such a work; it is easy to find as much or as little introductory material as needed." (R. Dawson, Zentralblatt MATH, 2001)


Table of contents (31 chapters)

  • Outline of the Book

    Deza, Michel Marie (et al.)

    Pages 1-10

  • Basic Definitions

    Deza, Michel Marie (et al.)

    Pages 11-22

  • Preliminaries on Distances

    Deza, Michel Marie (et al.)

    Pages 27-35

  • The Cut Cone and ℓ 1-Metrics

    Deza, Michel Marie (et al.)

    Pages 37-52

  • The Correlation Cone and {0,1}-Covariances

    Deza, Michel Marie (et al.)

    Pages 53-65

Buy this book

eBook $119.00
price for USA (gross)
  • ISBN 978-3-642-04295-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $229.00
price for USA
  • ISBN 978-3-540-61611-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.00
price for USA
  • ISBN 978-3-642-04294-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Geometry of Cuts and Metrics
Authors
Series Title
Algorithms and Combinatorics
Series Volume
15
Copyright
1997
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-04295-9
DOI
10.1007/978-3-642-04295-9
Hardcover ISBN
978-3-540-61611-5
Softcover ISBN
978-3-642-04294-2
Series ISSN
0937-5511
Edition Number
1
Number of Pages
XII, 588
Topics