Editorial Review:
This book offers an in-depth overview of polyhedral methods and efficient algorithms in combinatorial optimization.These methods form a broad, coherent and powerful kernel in combinatorial optimization, with strong links to discrete mathematics, mathematical programming and computer science. In eight parts, various areas are treated, each starting with an elementary introduction to the area, with short, elegant proofs of the principal results, and each evolving to the more advanced methods and results, with full proofs of some of the deepest theorems in the area. Over 4000 references to further research are given, and historical surveys on the basic subjects are presented.
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A encyclopaedic reference on combinatorial optimization 2004-01-05
A definitive account of the history and present state of combinatorial optimization from an author who is one of the most respected researchers in this area. The author has won the Dantzig award, the Fulkerson prize (twice) and the Lanchester Prize for his earlier classic text on "Theory of Linear and Integer Programming". Given the current pricing, it is a steal with over 1800 pages spread across three volumes. This is certainly not a text to be read from cover to cover but is a handy reference if you are interested in combinatorial optimization as a research topic or in the related areas of optimization, integer programming, polyhedral combinatorics, or graph theory.The author gives short and elegants proof of most of the results. The reader is expected to have a background in graph theory, linear programming and integer programming. The author cites some results without proofs from his earlier books , "Theory of Linear and Integer Programming", and "Geometric Algorithms and Combinatorial Optimization". The book does not concentrate on applications and modeling aspects of combinatorial optimization problems and it does not dwell on the computational methods for NP-hard problems. The book does not offer exercises but lists some open problems and research topics (updated on author's website). The book is mainly devoted to the theoretical developments in this field. Quoting the author, "We aim at offering an introduction and an in-depth survey of polyhedral combinatorics and efficient algorithms ... In the astonishing event that NP=P will be proved, this book will be highly incomplete". The results in this book are up to date till 2002 (updates are available at the author's website). In short this book should be invaluable for a graduate student or a researcher.
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