Algorithms and Combinatorics

Geometric Algorithms and Combinatorial Optimization

Authors: Grötschel, Martin, Lovasz, Laszlo, Schrijver, Alexander

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eBook $109.00
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  • ISBN 978-3-642-78240-4
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Softcover $149.00
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  • ISBN 978-3-642-78242-8
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About this book

Since the publication of the first edition of our book, geometric algorithms and combinatorial optimization have kept growing at the same fast pace as before. Nevertheless, we do not feel that the ongoing research has made this book outdated. Rather, it seems that many of the new results build on the models, algorithms, and theorems presented here. For instance, the celebrated Dyer-Frieze-Kannan algorithm for approximating the volume of a convex body is based on the oracle model of convex bodies and uses the ellipsoid method as a preprocessing technique. The polynomial time equivalence of optimization, separation, and membership has become a commonly employed tool in the study of the complexity of combinatorial optimization problems and in the newly developing field of computational convexity. Implementations of the basis reduction algorithm can be found in various computer algebra software systems. On the other hand, several of the open problems discussed in the first edition are still unsolved. For example, there are still no combinatorial polynomial time algorithms known for minimizing a submodular function or finding a maximum clique in a perfect graph. Moreover, despite the success of the interior point methods for the solution of explicitly given linear programs there is still no method known that solves implicitly given linear programs, such as those described in this book, and that is both practically and theoretically efficient. In particular, it is not known how to adapt interior point methods to such linear programs.

Table of contents (11 chapters)

  • Mathematical Preliminaries

    Grötschel, Martin (et al.)

    Pages 1-20

  • Complexity, Oracles, and Numerical Computation

    Grötschel, Martin (et al.)

    Pages 21-45

  • Algorithmic Aspects of Convex Sets: Formulation of the Problems

    Grötschel, Martin (et al.)

    Pages 46-63

  • The Ellipsoid Method

    Grötschel, Martin (et al.)

    Pages 64-101

  • Algorithms for Convex Bodies

    Grötschel, Martin (et al.)

    Pages 102-132

Buy this book

eBook $109.00
price for Mexico (gross)
  • ISBN 978-3-642-78240-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $149.00
price for Mexico
valid through 5 de noviembre de 2017
  • ISBN 978-3-642-78242-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Geometric Algorithms and Combinatorial Optimization
Authors
Series Title
Algorithms and Combinatorics
Series Volume
2
Copyright
1993
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-78240-4
DOI
10.1007/978-3-642-78240-4
Softcover ISBN
978-3-642-78242-8
Series ISSN
0937-5511
Edition Number
2
Number of Pages
XII, 362
Topics