Polytopes - Combinatorics and Computation (Oberwolfach Seminars)
Contributors: Gil Kalai (Editor); Günter M. Ziegler (Editor)
Edition: 1 edition
Publisher: Birkhäuser Basel; Birkhäuser
Published: September 6, 2000
Language: eng
Format: Paperback
Number of pages: 225
ISBN-13: 9783764363512
Subjects: Algebraic geometry; Algorithms & procedures; Combinatorics & graph theory; Optimization; Geometry - Algebraic; Discrete Mathematics (Computer Science); Geometry; Mathematics; Science/Mathematics; Geometry - General; Combinatorics; General; Diskrete Mathematik; Geometrie; Mathematics / General; Optimisierung; Computer Science
First sentence: Despite this (and to demonstrate this), our discussion in various lectures will take the low-dimensional situation as a starting point, and as a point of reference.
Description: 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.