Title | Polytopes โ{128}{148} Combinatorics and Computation [electronic resource] / edited by Gil Kalai, Gรผnter M. Ziegler |
---|---|

Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2000 |

Connect to | http://dx.doi.org/10.1007/978-3-0348-8438-9 |

Descript | VI, 225 p. 14 illus. online resource |

SUMMARY

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

CONTENT

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 Levinโ{128}{153}s Simplices Method

Mathematics
Geometry
Mathematics
Geometry