Cuts and metrics are well-known objects that arise-- independently, but with many deep and fascinating connections--in diverse fields. This book presents a wealth of results, from different mathematical disciplines, in a unified comprehensive manner.

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.

Includes supplementary material: sn.pub/extras

Inhalt
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.