Polytopes - Combinations and Computation

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Gil Kalai, Günter M. Ziegler
Springer Science & Business Media, 1 авг. 2000 г. - Всего страниц: 225
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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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Lectures on 01Polytopes
1
a Framework for Analyzing Convex Polytopes
43
Flag Numbers and FLAGTOOL
75
A Census of Flagvectors of 4Polytopes
105
Extremal Properties of 01Polytopes of Dimension 5
111
A Practical Study
131
Reconstructing a Simple Polytope from its Graph
155
Reconstructing a Nonsimple Polytope from its Graph
167
A Revised Implementation of the Reverse Search Vertex Enumeration Algorithm
177
The Complexity of Yamnitsky and Levins Simplices Algorithm
199
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