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Geometry of Cuts and Metrics
Overview of attention for book
Table of Contents
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Book Overview
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Chapter 1
Outline of the Book
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Chapter 2
Basic Definitions
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Chapter 3
Preliminaries on Distances
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Chapter 4
The Cut Cone and ℓ 1 -Metrics
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Chapter 5
The Correlation Cone and {0,1}-Covariances
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Chapter 6
Conditions for L 1 -Embeddability
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Chapter 7
Operations
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Chapter 8
L 1 -Metrics from Lattices, Semigroups and Normed Spaces
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Chapter 9
Metric Transforms of L 1 -Spaces
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Chapter 10
Lipschitz Embeddings
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Chapter 11
Dimensionality Questions for ℓ 1 -Embeddings
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Chapter 12
Examples of the Use of the L 1 -Metric
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Chapter 13
Preliminaries on Lattices
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Chapter 14
Hypermetrics and Delaunay Polytopes
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Chapter 15
Delaunay Polytopes: Rank and Hypermetric Faces
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Chapter 16
Extreme Delaunay Polytopes
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Chapter 17
Hypermetric Graphs
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Chapter 18
Preliminaries on Graphs
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Chapter 19
Isometric Embeddings of Graphs into Hypercubes
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Chapter 20
Isometric Embeddings of Graphs into Cartesian Products
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Chapter 21
ℓ 1 -Graphs
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Chapter 22
Rigidity of the Equidistant Metric
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Chapter 23
Hypercube Embeddings of the Equidistant Metric
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Chapter 24
Recognition of Hypercube Embeddable Metrics
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Chapter 25
Cut Lattices, Quasi h -Distances and Hilbert Bases
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Chapter 26
Operations on Valid Inequalities and Facets
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Chapter 27
Triangle Inequalities
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Chapter 28
Hypermetric Inequalities
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Chapter 29
Clique-Web Inequalities
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Chapter 30
Other Valid Inequalities and Facets
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Chapter 31
Geometric Properties
Overall attention for this book and its chapters
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Book overview
1. Outline of the Book
2. Basic Definitions
3. Preliminaries on Distances
4. The Cut Cone and ℓ 1 -Metrics
5. The Correlation Cone and {0,1}-Covariances
6. Conditions for L 1 -Embeddability
7. Operations
8. L 1 -Metrics from Lattices, Semigroups and Normed Spaces
9. Metric Transforms of L 1 -Spaces
10. Lipschitz Embeddings
11. Dimensionality Questions for ℓ 1 -Embeddings
12. Examples of the Use of the L 1 -Metric
13. Preliminaries on Lattices
14. Hypermetrics and Delaunay Polytopes
15. Delaunay Polytopes: Rank and Hypermetric Faces
16. Extreme Delaunay Polytopes
17. Hypermetric Graphs
18. Preliminaries on Graphs
19. Isometric Embeddings of Graphs into Hypercubes
20. Isometric Embeddings of Graphs into Cartesian Products
21. ℓ 1 -Graphs
22. Rigidity of the Equidistant Metric
23. Hypercube Embeddings of the Equidistant Metric
24. Recognition of Hypercube Embeddable Metrics
25. Cut Lattices, Quasi h -Distances and Hilbert Bases
26. Operations on Valid Inequalities and Facets
27. Triangle Inequalities
28. Hypermetric Inequalities
29. Clique-Web Inequalities
30. Other Valid Inequalities and Facets
31. Geometric Properties
Summary
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