Geometric Algorithms and Combinatorial Optimization
Martin Grötschel
ISBN 10: 3642782426 ISBN 13: 9783642782428
Verlag: Springer, Springer Gabler Dez 2011, 2011
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This item is printed on demand - Print on Demand Titel. Neuware -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).Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 380 pp. Englisch. Bestandsnummer des Verkäufers 9783642782428
Inhaltsangabe:
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).
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Bibliografische Details
Titel: Geometric Algorithms and Combinatorial ...
Verlag: Springer, Springer Gabler Dez 2011
Erscheinungsdatum: 2011
Einband: Taschenbuch
Zustand: Neu
Auflage: 2. Auflage
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Geometric Algorithms and Combinatorial Optimization
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Geometric Algorithms and Combinatorial Optimization
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 Nevertheless, we do not feel that the ongoing research has made this book outdated.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. Artikel-Nr. 9783642782428
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Geometric Algorithms and Combinatorial Optimization (Algorithms and Combinatorics)
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Paperback. Zustand: Brand New. 2nd edition. 374 pages. 9.61x0.87x6.69 inches. In Stock. Artikel-Nr. x-3642782426
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