Buch, Englisch, Band 15, 588 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1062 g
Reihe: Algorithms and Combinatorics
Buch, Englisch, Band 15, 588 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1062 g
Reihe: Algorithms and Combinatorics
ISBN: 978-3-540-61611-5
Verlag: Springer Berlin Heidelberg
Cuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, combinatorial matrix theory, statistical physics, VLSI design etc.
This book presents a wealth of results, from different mathematical disciplines, in a unified comprehensive manner, and establishes new and old links, which cannot be found elsewhere. It provides a unique and invaluable source for researchers and graduate students.
From the Reviews:
"This book is definitely a milestone in the literature of integer programming and combinatorial optimization. It draws from the Interdisciplinarity of these fields […]. With knowledge about the relevant terms, one can enjoy special subsections without being entirely familiar with the rest of the chapter. This makes it not only an interesting research book but even a dictionary. […] The longer one works with it, the more beautiful it becomes." Optima 56, 1997.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Operations Research Graphentheorie
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
- Mathematik | Informatik Mathematik Geometrie
- Mathematik | Informatik EDV | Informatik Informatik Theoretische Informatik
Weitere Infos & Material
Outline of the Book.- I.Measure Aspects: El-Embeddability and Probability.- Preliminaries on Distances.- The Cut Cone and #x2113;-Metrics.- The Correlation Cone and {0. 1}-Covariances.- Conditions for -Embeddability.- Operations.- -Metrics from Lattices, Semigroups and Normed Spaces.- Metric Transforms of -Spaces.- Lipschitz Embeddings.- Dimensionality Questions for -Embeddings.- Examples of the Use of the -Metric.- Basic Definitions.- I1.Hypermetric Spaces: an Approach via Geometry of Numbers.- Preliminaries on Lattices.- Hypermetrics and Delaunay Polytopes.- Delaunay Polytopes: Rank and Hypermetric Faces.- Extreme Delaunay Polytopes.- Hypermetric Graphs.- I11.Isometric Embeddings of Graphs.- Preliminaries on Graphs.- Isometric Embeddings of Graphs into Hypercubes.- Isometric Embeddings of Graphs into Cartesian Products.- -Graphs.- IV.Hypercube Embeddings and Designs.- Rigidity of the Equidistant Metric.- Hypercube Embeddings of the Equidistant Metric.- Recognition of Hypercube Embeddable Metrics.- Cut Lattices, Quasi -Distances and Hilbert Bases.- V.Facets of the Cut Cone and Polytope.- Operations on Valid Inequalities and Facets.- Triangle Inequalities.- Hypermetric Inequalities.- Clique-Web Inequalities.- Other Valid Inequalities and Facets.- Geometric Properties.
