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Geometry of Cuts and Metrics

  • Michel Marie Deza
  • Monique Laurent

Part of the Algorithms and Combinatorics book series (AC, volume 15)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Michel Marie Deza, Monique Laurent
    Pages 1-10
  3. Michel Marie Deza, Monique Laurent
    Pages 11-22
  4. Measure Aspects: ℓ 1-Embeddability and Probability

    1. Front Matter
      Pages 23-26
    2. Michel Marie Deza, Monique Laurent
      Pages 27-35
    3. Michel Marie Deza, Monique Laurent
      Pages 37-52
    4. Michel Marie Deza, Monique Laurent
      Pages 53-65
    5. Michel Marie Deza, Monique Laurent
      Pages 67-92
    6. Michel Marie Deza, Monique Laurent
      Pages 93-104
    7. Michel Marie Deza, Monique Laurent
      Pages 105-111
    8. Michel Marie Deza, Monique Laurent
      Pages 113-124
    9. Michel Marie Deza, Monique Laurent
      Pages 125-137
    10. Michel Marie Deza, Monique Laurent
      Pages 139-159
    11. Michel Marie Deza, Monique Laurent
      Pages 161-166
  5. Hypermetric Spaces: an Approach via Geometry of Numbers

    1. Front Matter
      Pages 167-174
    2. Michel Marie Deza, Monique Laurent
      Pages 175-192
    3. Michel Marie Deza, Monique Laurent
      Pages 193-216
    4. Michel Marie Deza, Monique Laurent
      Pages 217-233
    5. Michel Marie Deza, Monique Laurent
      Pages 235-250
    6. Michel Marie Deza, Monique Laurent
      Pages 251-273
  6. Isometric Embeddings of Graphs

    1. Front Matter
      Pages 275-278
    2. Michel Marie Deza, Monique Laurent
      Pages 279-281
    3. Michel Marie Deza, Monique Laurent
      Pages 283-295
    4. Michel Marie Deza, Monique Laurent
      Pages 297-311
    5. Michel Marie Deza, Monique Laurent
      Pages 313-330
  7. Hypercube Embeddings and Designs

    1. Front Matter
      Pages 331-334
    2. Michel Marie Deza, Monique Laurent
      Pages 335-340
    3. Michel Marie Deza, Monique Laurent
      Pages 341-352
    4. Michel Marie Deza, Monique Laurent
      Pages 353-380
    5. Michel Marie Deza, Monique Laurent
      Pages 381-393
  8. Facets of the Cut Cone and Polytope

    1. Front Matter
      Pages 395-400
    2. Michel Marie Deza, Monique Laurent
      Pages 401-419
    3. Michel Marie Deza, Monique Laurent
      Pages 421-444
    4. Michel Marie Deza, Monique Laurent
      Pages 445-465
    5. Michel Marie Deza, Monique Laurent
      Pages 467-485
    6. Michel Marie Deza, Monique Laurent
      Pages 487-509
    7. Michel Marie Deza, Monique Laurent
      Pages 511-550
  9. Back Matter
    Pages 551-588

About this book

Introduction

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

Keywords

Geometrie von Polyedern Geometrie von Zahlen Graph Graph theory Notation Polyederkombinatorik combinatorial optimization discrete metric spaces diskrete metrische Räume geometry of numbers geometry of polyhedra kombinatorische Optimierung optimization polyhedral combinator

Authors and affiliations

  • Michel Marie Deza
    • 1
    • 2
  • Monique Laurent
    • 1
    • 3
  1. 1.Département de Mathématiques et d’InformatiqueLaboratoire d’Informatique de l’Ecole Normale SupérieureParis Cedex 05France
  2. 2.Department of MathematicsMoscow Pedagogical State UniversityMoscowRussia
  3. 3.CWIAmsterdamThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-04295-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 1997
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-04294-2
  • Online ISBN 978-3-642-04295-9
  • Series Print ISSN 0937-5511
  • Series Online ISSN 2197-6783
  • Buy this book on publisher's site
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