Polytopes - Combinations and Computation

Polytopes - Combinations and Computation
Author :
Publisher : Birkhäuser
Total Pages : 228
Release :
ISBN-10 : 9783034884389
ISBN-13 : 3034884389
Rating : 4/5 (89 Downloads)

Book Synopsis Polytopes - Combinations and Computation by : Gil Kalai

Download or read book Polytopes - Combinations and Computation written by Gil Kalai and published by Birkhäuser. This book was released on 2012-12-06 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


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Many polytopes of practical interest have enormous output complexity and are often highly degenerate, posing severe difficulties for known general-purpose algor