Geometric algorithms combinatorial optimization (14 Ergebnisse)
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gebundene Ausgabe. Zustand: Gut. 2. Auflage.. 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 Sp…rache. Sprache: Englisch Gewicht in Gramm: 750.
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First Edition. Library copy - library marks remain. Very good copy in the original title-blocked cloth. Slight suggestion only of dust-dulling to the spine bands and panel edges. Remains particularly well-preserved overall; tight, bright, clean and strong. Physical description: XII, 362p. 23 illus. Notes: Bibliographic Level Mod…e of Issuance: MonographIncludes bibliographical references and index. Contents: 0. Mathematical Preliminaries -- 0.1 Linear Algebra and Linear Programming -- 0.2 Graph Theory -- 1. Complexity, Oracles, and Numerical Computation -- 1.1 Complexity Theory: P and NP -- 1.2 Oracles -- 1.3 Approximation and Computation of Numbers -- 1.4 Pivoting and Related Procedures -- 2. Algorithmic Aspects of Convex Sets: Formulation of the Problems -- 2.1 Basic Algorithmic Problems for Convex Sets -- 2.2 Nondeterministic Decision Problems for Convex Sets -- 3. The Ellipsoid Method -- 3.1 Geometric Background and an Informal Description -- 3.2 The Central-Cut Ellipsoid Method -- 3.3 The Shallow-Cut Ellipsoid Method -- 4. Algorithms for Convex Bodies -- 4.1 Summary of Results -- 4.2 Optimization from Separation -- 4.3 Optimization from Membership -- 4.4 Equivalence of the Basic Problems -- 4.5 Some Negative Results -- 4.6 Further Algorithmic Problems for Convex Bodies -- 4.7 Operations on Convex Bodies -- 5. Diophantine Approximation and Basis Reduction -- 5.1 Continued Fractions -- 5.2 Simultaneous Diophantine Approximation: Formulation of the Problems -- 5.3 Basis Reduction in Lattices -- 5.4 More on Lattice Algorithms -- 6. Rational Polyhedra -- 6.1 Optimization over Polyhedra: A Preview -- 6.2 Complexity of Rational Polyhedra -- 6.3 Weak and Strong Problems -- 6.4 Equivalence of Strong Optimization and Separation -- 6.5 Further Problems for Polyhedra -- 6.6 Strongly Polynomial Algorithms -- 6.7 Integer Programming in Bounded Dimension -- 7. Combinatorial Optimization: Some Basic Examples. -- 7.1 Flows and Cuts -- 7.2 Arborescences -- 7.3 Matching -- 7.4 Edge Coloring -- 7.5 Matroids -- 7.6 Subset Sums -- 7.7 Concluding Remarks -- 8. Combinatorial Optimization: A Tour d'Horizon -- 8.1 Blocking Hypergraphs and Polyhedra -- 8.2 Problems on Bipartite Graphs -- 8.3 Flows, Paths, Chains, and Cuts -- 8.4 Trees, Branchings, and Rooted and Directed Cuts -- 8.5 Matchings, Odd Cuts, and Generalizations -- 8.6 Multicommodity Flows -- 9. Stable Sets in Graphs -- 9.1 Odd Circuit Constraints and t-Perfect Graphs -- 9.2 Clique Constraints and Perfect Graphs -- 9.3 Orthonormal Representations -- 9.4 Coloring Perfect Graphs -- 9.5 More Algorithmic Results on Stable Sets -- 10. Submodular Functions -- 10.1 Submodular Functions and Polymatroids -- 10.2 Algorithms for Polymatroids and Submodular Functions -- 10.3 Submodular Functions on Lattice, Intersecting, and Crossing Families -- 10.4 Odd Submodular Function Minimization and Extensions -- References -- Notation Index -- Author Index. Subjects: Combinatorial geometry.Geometry of numbers.Mathematical optimization.Combinatorial geometry.Geometry of numbers.Mathematical optimization.Programming (Mathematics)Combinatorial geometry.Geometry of numbers.Mathematical optimization.Programming (Mathematics)Mathematics. Combinatorial analysis.Combinatorial analysis.Mathematics.Combinatorics. 1 Kg.
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First Edition. Library copy - library marks remain. Very good copy in the original title-blocked cloth. Slight suggestion only of dust-dulling to the spine bands and panel edges. Remains particularly well-preserved overall; tight, bright, clean and strong. Physical description: XII, 362p. 23 illus. Notes: Bibliographic Level Mod…e of Issuance: MonographIncludes bibliographical references and index. Contents: 0. Mathematical Preliminaries -- 0.1 Linear Algebra and Linear Programming -- 0.2 Graph Theory -- 1. Complexity, Oracles, and Numerical Computation -- 1.1 Complexity Theory: P and NP -- 1.2 Oracles -- 1.3 Approximation and Computation of Numbers -- 1.4 Pivoting and Related Procedures -- 2. Algorithmic Aspects of Convex Sets: Formulation of the Problems -- 2.1 Basic Algorithmic Problems for Convex Sets -- 2.2 Nondeterministic Decision Problems for Convex Sets -- 3. The Ellipsoid Method -- 3.1 Geometric Background and an Informal Description -- 3.2 The Central-Cut Ellipsoid Method -- 3.3 The Shallow-Cut Ellipsoid Method -- 4. Algorithms for Convex Bodies -- 4.1 Summary of Results -- 4.2 Optimization from Separation -- 4.3 Optimization from Membership -- 4.4 Equivalence of the Basic Problems -- 4.5 Some Negative Results -- 4.6 Further Algorithmic Problems for Convex Bodies -- 4.7 Operations on Convex Bodies -- 5. Diophantine Approximation and Basis Reduction -- 5.1 Continued Fractions -- 5.2 Simultaneous Diophantine Approximation: Formulation of the Problems -- 5.3 Basis Reduction in Lattices -- 5.4 More on Lattice Algorithms -- 6. Rational Polyhedra -- 6.1 Optimization over Polyhedra: A Preview -- 6.2 Complexity of Rational Polyhedra -- 6.3 Weak and Strong Problems -- 6.4 Equivalence of Strong Optimization and Separation -- 6.5 Further Problems for Polyhedra -- 6.6 Strongly Polynomial Algorithms -- 6.7 Integer Programming in Bounded Dimension -- 7. Combinatorial Optimization: Some Basic Examples. -- 7.1 Flows and Cuts -- 7.2 Arborescences -- 7.3 Matching -- 7.4 Edge Coloring -- 7.5 Matroids -- 7.6 Subset Sums -- 7.7 Concluding Remarks -- 8. Combinatorial Optimization: A Tour d'Horizon -- 8.1 Blocking Hypergraphs and Polyhedra -- 8.2 Problems on Bipartite Graphs -- 8.3 Flows, Paths, Chains, and Cuts -- 8.4 Trees, Branchings, and Rooted and Directed Cuts -- 8.5 Matchings, Odd Cuts, and Generalizations -- 8.6 Multicommodity Flows -- 9. Stable Sets in Graphs -- 9.1 Odd Circuit Constraints and t-Perfect Graphs -- 9.2 Clique Constraints and Perfect Graphs -- 9.3 Orthonormal Representations -- 9.4 Coloring Perfect Graphs -- 9.5 More Algorithmic Results on Stable Sets -- 10. Submodular Functions -- 10.1 Submodular Functions and Polymatroids -- 10.2 Algorithms for Polymatroids and Submodular Functions -- 10.3 Submodular Functions on Lattice, Intersecting, and Crossing Families -- 10.4 Odd Submodular Function Minimization and Extensions -- References -- Notation Index -- Author Index. Subjects: Combinatorial geometry.Geometry of numbers.Mathematical optimization.Combinatorial geometry.Geometry of numbers.Mathematical optimization.Programming (Mathematics)Combinatorial geometry.Geometry of numbers.Mathematical optimization.Programming (Mathematics)Mathematics. Combinatorial analysis.Combinatorial analysis.Mathematics.Combinatorics. 1 Kg.
- Softcover
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Hardcover. Zustand: Good. X_Library copy with light corner wear. I found no text marks. Good clean used book.
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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.
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Paperback. Zustand: Brand New. 2nd edition. 374 pages. 9.61x0.87x6.69 inches. In Stock.
- Hardcover
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Zustand: gut. 1993. Geometric Algorithms and Combinatorial Optimization Algorithms and Combinatorics, 2 In deutscher Sprache. pages.
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hardcover. Zustand: Very Good. Very Good. Dust Jacket may NOT BE INCLUDED.CDs may be missing. SHIPS FROM MULTIPLE LOCATIONS. book.
Verlag: Springer, 1988
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In den WarenkorbFirst Edition XII + 362 p., tables, formulas, bibliogr., index. (Orig. hardback. AS NEW) RARE AND SOUGHT AFTER EDITION 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.
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Zustand: new. Questo è un articolo print on demand.
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Taschenbuch. Zustand: 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 o…utdated. 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.
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Zustand: 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 m…ade this book outdated. Rather, it see.
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Taschenbuch. Zustand: Neu. 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 o…f 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.
