Geometric Algorithms and Combinatorial Optimization Algorithms and Combinatorics, 2

Grötschel, Martin, Laszlo Lovasz and Alexander Schrijver:

ISBN 10: 3540567402 / ISBN 13: 9783540567400

Verlag: Springer, 1993

Beschreibung

362 Seiten Das hier angebotene Buch stammt aus einer teilaufgelösten Bibliothek und kann die entsprechenden Kennzeichnungen aufweisen (Rückenschild, Instituts-Stempel.); der Buchzustand ist ansonsten ordentlich und dem Alter entsprechend gut. Einband folienkaschiert. In ENGLISCHER Sprache. Sprache: Englisch Gewicht in Gramm: 750.

Bestandsnummer des Verkäufers 2220370

Bibliografische Details

• Titel: Geometric Algorithms and Combinatorial Optimization Algorithms and Combinatorics, 2
• Verlag: Springer
• Erscheinungsjahr: 1993
• Sprache: Englisch
• ISBN-10: 3540567402
• ISBN-13: 9783540567400
• Einband: gebundene Ausgabe
• Auflage: 2. Auflage;.
• Zustand: Gut
• Verkäuferkataloge:
  • 200 Mathematik

Über diesen Titel

Inhaltsangabe

This book develops geometric techniques for proving the polynomial time solvability of problems in convexity theory, geometry, and, in particular, combinatorial optimization. It offers a unifying approach which is based on two fundamental geometric algorithms: the ellipsoid method for finding a point in a convex set and the basis reduction method for point lattices. This 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. The first edition of this book was received enthusiastically by the community of discrete mathematicians, combinatorial optimizers, operations researchers, and computer scientists. To quote just from a few reviews: "The book is written in a very grasping way, legible both for people who are interested in the most important results and for people who are interested in technical details and proofs." #manuscripta geodaetica#1

Reseña del editor

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 Nevertheless, we do not feel that the ongoing research has made this book outdated.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.