Polytopes - Combinations and Computation

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

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.

• Diskrete Mathematik
• Geometrie
• Optimisierung
• addition
• boundary element method
• combinatorial optimization
• computational geometry
• computer
• extrema
• graph
• implementation
• linear optimization
• optimization
• programming
• scientific computing

• 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

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