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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, distance geometry, combinatorial matrix theory, statistical physics, VLSI design etc. A main feature of this book is its interdisciplinarity. The book contains a wealth of results, from different mathematical disciplines, which are presented here in a unified and comprehensive manner. Geometric representations and methods turn out to be the linking theme. This book will provide 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 as it gathers methods and results from polytope theory, geometry of numbers, probability theory, design and graph theory around two objects, cuts and metrics. [… ] The book is very nicely written [… ] The book is also very well structured. 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. [… ] In my opinion, the book is a beautiful piece of work. The longer one works with it, the more beautiful it becomes." Robert Weismantel, Optima 56 (1997) "… In short, this is a very interesting book which is nice to have." Alexander I. Barvinok, MR 1460488 (98g:52001) "… This is a large and fascinating book. As befits a book which contains material relevant to so many areas of mathematics (and related disciplines such as statistics, physics, computing science, and economics), it is self-contained and written in a readable style. Moreover, the index, bibliography, and table of contents are all that they should be in such a work; it is easy to find as much or as little introductory material as needed." R.Dawson, Zentralblatt MATH Database 0885.52001.

Discrete mathematics --- Graph theory --- Metric spaces --- Embeddings (Mathematics) --- Théorie des graphes --- Espaces métriques --- Plongements (Mathématiques) --- Graph theory. --- Metric spaces. --- Embeddings (Mathematics). --- Théorie des graphes --- Espaces métriques --- Plongements (Mathématiques) --- Discrete mathematics. --- Geometry. --- Combinatorics. --- Convex geometry . --- Discrete geometry. --- Number theory. --- Discrete Mathematics. --- Graph Theory. --- Convex and Discrete Geometry. --- Number Theory. --- Number study --- Numbers, Theory of --- Algebra --- Geometry --- Combinatorial geometry --- Combinatorics --- Mathematical analysis --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Mathematics --- Euclid's Elements --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Extremal problems

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The last decade has seen two parallel developments, one in computer science, the other in mathematics, both dealing with the same kind of combinatorial structures: networks with strong symmetry properties or, in graph-theoretical language, vertex-transitive graphs, in particular their prototypical examples, Cayley graphs. In the design of large interconnection networks it was realised that many of the most fre­ quently used models for such networks are Cayley graphs of various well-known groups. This has spawned a considerable amount of activity in the study of the combinatorial properties of such graphs. A number of symposia and congresses (such as the bi-annual IWIN, starting in 1991) bear witness to the interest of the computer science community in this subject. On the mathematical side, and independently of any interest in applications, progress in group theory has made it possible to make a realistic attempt at a complete description of vertex-transitive graphs. The classification of the finite simple groups has played an important role in this respect.

Cayley graphs --- Group theory --- Congresses --- Discrete mathematics. --- Computer science—Mathematics. --- Group theory. --- Computer communication systems. --- Combinatorics. --- Microprocessors. --- Discrete Mathematics. --- Discrete Mathematics in Computer Science. --- Group Theory and Generalizations. --- Computer Communication Networks. --- Processor Architectures. --- Minicomputers --- Combinatorics --- Algebra --- Mathematical analysis --- Communication systems, Computer --- Computer communication systems --- Data networks, Computer --- ECNs (Electronic communication networks) --- Electronic communication networks --- Networks, Computer --- Teleprocessing networks --- Data transmission systems --- Digital communications --- Electronic systems --- Information networks --- Telecommunication --- Cyberinfrastructure --- Electronic data processing --- Network computers --- Groups, Theory of --- Substitutions (Mathematics) --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Distributed processing --- Cayley graphs. --- Cayley color graphs --- Cayley color groups --- Cayley diagrams --- Cayley's color graphs --- Cayley's color groups --- Cayley's diagrams --- Cayley's graphs --- Color graphs, Cayley --- Color groups, Cayley --- Dehnsche Gruppenbild --- Diagrams, Cayley --- Gruppenbild, Dehnsche --- Graph theory --- Graphes, Théorie des

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This book constitutes the strictly refereed post-conference proceedings of the 5th International Symposium on Graph Drawing, GD'97, held in Rome, Italy, in September 1997. The 33 revised full papers and 10 systems demonstrations presented were selected from 80 submissions. The topics covered include planarity, crossing theory, three dimensional representations, orthogonal representations, clustering and labeling problems, packing problems, general methodologies, and systems and applications.

Computer graphics --- Graph theory --- Congresses. --- Technology - General --- Engineering & Applied Sciences --- Congresses --- Computer science. --- Computers. --- Algorithms. --- Computer science --- Computer-aided engineering. --- Discrete mathematics. --- Combinatorics. --- Computer Science. --- Theory of Computation. --- Discrete Mathematics. --- Computer-Aided Engineering (CAD, CAE) and Design. --- Discrete Mathematics in Computer Science. --- Algorithm Analysis and Problem Complexity. --- Mathematics. --- Information theory. --- Computer aided design. --- Computational complexity. --- Computer software. --- Software, Computer --- Computer systems --- Complexity, Computational --- Electronic data processing --- Machine theory --- CAD (Computer-aided design) --- Computer-assisted design --- Computer-aided engineering --- Design --- Communication theory --- Communication --- Cybernetics --- Combinatorics --- Algebra --- Mathematical analysis --- Computer science—Mathematics. --- Algorism --- Arithmetic --- CAE --- Engineering --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Calculators --- Cyberspace --- Foundations --- Data processing --- Computer graphics - Congresses. --- Graph theory - Congresses.