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Polytopes - Combinations and Computation

  • Book
  • © 2000

Overview

Editors:
  1. Gil Kalai

    1. Institute of Mathematics and Computer Science, The Hebrew University, Jerusalem, Israel

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    You can also search for this editor in PubMed   Google Scholar

  2. Günter M. Ziegler

    1. Fachbereich Mathematik MA 7-1, Technische Universität Berlin, Berlin, Germany

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Oberwolfach Seminars (OWS, volume 29)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-vi
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  2. Lectures on 0/1-Polytopes

    • Günter M. Ziegler
    Pages 1-41

  3. polymake: a Framework for Analyzing Convex Polytopes

    • Ewgenij Gawrilow, Michael Joswig
    Pages 43-73

  4. Flag Numbers and FLAGTOOL

    • Gil Kalai, Peter Kleinschmidt, Günter Meisinger
    Pages 75-103

  5. A Census of Flag-vectors of 4-Polytopes

    • Andrea Höppner, Günter M. Ziegler
    Pages 105-110

  6. Extremal Properties of 0/1-Polytopes of Dimension 5

    • Oswin Aichholzer
    Pages 111-130

  7. Exact Volume Computation for Polytopes: A Practical Study

    • Benno Büeler, Andreas Enge, Komei Fukuda
    Pages 131-154

  8. Reconstructing a Simple Polytope from its Graph

    • Hans Achatz, Peter Kleinschmidt
    Pages 155-165

  9. Reconstructing a Non-simple Polytope from its Graph

    • Michael Joswig
    Pages 167-176

  10. A Revised Implementation of the Reverse Search Vertex Enumeration Algorithm

    • David Avis
    Pages 177-198

  11. The Complexity of Yamnitsky and Levin’s Simplices Algorithm

    • Sven G. Bartels
    Pages 199-225
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Keywords

About this book

Questions that arose from linear programming and combinatorial optimization have been a driving force for modern polytope theory, such as the diameter questions motivated by the desire to understand the complexity of the simplex algorithm, or the need to study facets for use in cutting plane procedures. In addition, algorithms now provide the means to computationally study polytopes, to compute their parameters such as flag vectors, graphs and volumes, and to construct examples of large complexity. The papers of this volume thus display a wide panorama of connections of polytope theory with other fields. Areas such as discrete and computational geometry, linear and combinatorial optimization, and scientific computing have contributed a combination of questions, ideas, results, algorithms and, finally, computer programs.

Editors and Affiliations

  • Institute of Mathematics and Computer Science, The Hebrew University, Jerusalem, Israel

    Gil Kalai

  • Fachbereich Mathematik MA 7-1, Technische Universität Berlin, Berlin, Germany

    Günter M. Ziegler

Bibliographic Information

  • Book Title: Polytopes - Combinations and Computation

  • Editors: Gil Kalai, Günter M. Ziegler

  • Series Title: Oberwolfach Seminars

  • DOI: https://doi.org/10.1007/978-3-0348-8438-9

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 2000

  • Softcover ISBN: 978-3-7643-6351-2Published: 01 August 2000

  • eBook ISBN: 978-3-0348-8438-9Published: 06 December 2012

  • Series ISSN: 1661-237X

  • Series E-ISSN: 2296-5041

  • Edition Number: 1

  • Number of Pages: VI, 225

  • Number of Illustrations: 14 b/w illustrations

  • Topics: Geometry

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