Geometry of Cuts and Metrics (Algorithms and Combinatorics) [Hardcover]

Michel Marie Deza (Author), Monique Laurent (Author)

Book Description

Publication Date: June 27, 1997 | ISBN-10: 354061611X | ISBN-13: 978-3540616115 | Edition: 1

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.

Editorial Reviews

Review

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 "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, 2001)

From the Back Cover

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

Product Details

• Hardcover: 599 pages
• Publisher: Springer; 1 edition (June 27, 1997)
• Language: English
• ISBN-10: 354061611X
• ISBN-13: 978-3540616115
• Product Dimensions: 9.1 x 6.3 x 1.6 inches
• Shipping Weight: 2.2 pounds (View shipping rates and policies)
• Amazon Best Sellers Rank: #3,804,156 in Books (See Top 100 in Books)

More About the Author

From Wikipedia, the free encyclopedia.

Michel Marie Deza is a French and Russian mathematician, specializing in Combinatorics, Discrete Geometry and Graph Theory. He is a retired director of research at the French National Centre for Scientific Research (CNRS), the vice president of the European Academy of Sciences, a research professor at the Japan Advanced Institute of Science and Technology, and the founding editor-in-chief of the European Journal of Combinatorics.