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).
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Présentation de l'éditeur
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
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Geometric Algorithms and Combinatorial Optimization
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Geometric Algorithms and Combinatorial Optimization
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Springer Berlin Heidelberg Dez 2011, 2011
ISBN 10 : 3642782426
ISBN 13 : 9783642782428
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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - 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 Nevertheless, we do not feel that the ongoing research has made this book outdated.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. 380 pp. Englisch. N° de réf. du vendeur 9783642782428
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Geometric Algorithms and Combinatorial Optimization
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Springer Berlin Heidelberg, 2011
ISBN 10 : 3642782426
ISBN 13 : 9783642782428
Neuf
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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 see. N° de réf. du vendeur 5070508
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Taschenbuch. Etat : Neu. Geometric Algorithms and Combinatorial Optimization | Martin Grötschel (u. a.) | Taschenbuch | XII | Englisch | 2011 | Springer | EAN 9783642782428 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. N° de réf. du vendeur 106366849
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Geometric Algorithms and Combinatorial Optimization
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Etat : New. pp. xii + 362 2nd Edition. N° de réf. du vendeur 2654507731
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Geometric Algorithms and Combinatorial Optimization
Edité par
Springer Berlin Heidelberg, Springer Berlin Heidelberg Dez 2011, 2011
ISBN 10 : 3642782426
ISBN 13 : 9783642782428
Neuf
Taschenbuch
Edition originale
Vendeur : buchversandmimpf2000, Emtmannsberg, BAYE, Allemagne
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Taschenbuch. Etat : Neu. 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. N° de réf. du vendeur 9783642782428
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Geometric Algorithms and Combinatorial Optimization
Edité par
Springer Berlin Heidelberg, 2011
ISBN 10 : 3642782426
ISBN 13 : 9783642782428
Neuf
Taschenbuch
Vendeur : AHA-BUCH GmbH, Einbeck, Allemagne
Évaluation du vendeur 5 sur 5 étoiles
Taschenbuch. Etat : 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. N° de réf. du vendeur 9783642782428
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Geometric Algorithms and Combinatorial Optimization
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Etat : New. Print on Demand pp. xii + 362 23 Figures. N° de réf. du vendeur 55052044
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