Polytopes - Combinatorics and Computation (Oberwolfach Seminars)

Gil Kalai, Gunter M. Ziegler

ISBN 10: 3764363517 / ISBN 13: 9783764363512

Editore: Birkhauser Basel 2008-10-10, 2008

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Codice articolo 6666-IUK-9783764363512

Dati bibliografici

• Titolo: Polytopes - Combinatorics and Computation (Oberwolfach Seminars)
• Editore: Birkhauser Basel 2008-10-10
• Data di pubblicazione: 2008
• Lingua: Inglese
• ISBN 10: 3764363517
• ISBN 13: 9783764363512
• Rilegatura: Paperback
• Condizione: New

Descrizione articolo

Riassunto

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.

Contenuti

Lectures on 0/l-Polytopes.- polymake: A Framework for Analyzing Convex Polytopes.- Flag Numbers and FLAGTOOL.- A Census of Flag-vectors of 4-Polytopes.- Extremal Properties of 0/1-Polytopes of Dimension 5.- Exact Volume Computation for Polytopes: A Practical Study.- Reconstructing a Simple Polytope from its Graph.- Reconstructing a Non-simple Polytope from its Graph.- A Revised Implementation of the Reverse Search Vertex Enumeration Algorithm.- The Complexity of Yamnitsky and Levin’s Simplices Method.