Geometric Algorithms and Combinatorial Optimization

Martin Grötschel

ISBN 10: 3642782426 / ISBN 13: 9783642782428

Published by Springer Berlin Heidelberg, Springer Berlin Heidelberg Dez 2011, 2011

About this Item

Neuware -Since the publication of the first edition of our book, geometric algorithms and combinatorial optimization have kept growing at the same fast pace as before. Nevertheless, we do not feel that the ongoing research has made this book outdated. Rather, it seems that many of the new results build on the models, algorithms, and theorems presented here. For instance, the celebrated Dyer-Frieze-Kannan algorithm for approximating the volume of a convex body is based on the oracle model of convex bodies and uses the ellipsoid method as a preprocessing technique. The polynomial time equivalence of optimization, separation, and membership has become a commonly employed tool in the study of the complexity of combinatorial optimization problems and in the newly developing field of computational convexity. Implementations of the basis reduction algorithm can be found in various computer algebra software systems. On the other hand, several of the open problems discussed in the first edition are still unsolved. For example, there are still no combinatorial polynomial time algorithms known for minimizing a submodular function or finding a maximum clique in a perfect graph. Moreover, despite the success of the interior point methods for the solution of explicitly given linear programs there is still no method known that solves implicitly given linear programs, such as those described in this book, and that is both practically and theoretically efficient. In particular, it is not known how to adapt interior point methods to such linear programs.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 380 pp. Englisch.

Seller Inventory # 9783642782428

Bibliographic Details

• Title: Geometric Algorithms and Combinatorial Optimization
• Publisher: Springer Berlin Heidelberg, Springer Berlin Heidelberg Dez 2011
• Publication Date: 2011
• Language: English
• ISBN 10: 3642782426
• ISBN 13: 9783642782428
• Binding: Taschenbuch
• Edition: 1st Edition
• Condition: Neu

About this title

Synopsis

This book develops geometric techniques for proving the polynomial time solvability of problems in convexity theory, geometry, and, in particular, combinatorial optimization. The book is a continuation and extension of previous research of the authors for which they received the Fulkerson prize, awarded by the Mathematical Programming Society and the American Mathematical Society. To quote from a review: "This book ... is doubtless one of the outstanding books in discrete mathematics at all." (Journal of Information Proceedings and Cybernetics).