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Combinatorial Optimization: Polyhedra and Efficiency (Algorithms and Combinatorics), by Alexander Schrijver
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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.
- Sales Rank: #12921136 in Books
- Published on: 2004-07-27
- Number of discs: 3
- Platforms: Windows 98, Windows Me, Windows 2000, Windows XP
- Original language: English
- Subtitled in: English
- Number of items: 3
- Dimensions: 5.00" h x 5.75" w x .50" l,
- Binding: CD-ROM
- 1882 pages
Review
Aus den Rezensionen:
"… ‘Effiziente Algorithmen‘ und ‘Kombinatorik der Polyeder‘ bilden ... den roten Faden durch das monumentale Werk ... Sehr knappe Einf�hrungen in das jeweilige Thema, ein paar einfache erste Resultate ... und dann eine enzykopl�dische [sic] Durchsicht der Methoden, Ideen, Varianten, Laufzeiten, mit einer �beraus detaillierten Literaturliste und historischen Zusammenfassung. Alles wird n�chtern … dargeboten … Man bl�ttert das Buch durch … und erkennt mit Respekt und Staunen, dass der Autor alles, aber auch wirklich alles durchgearbeitet hat - eine gro�e Leistung. … Ich kenne kein vergleichbares neueres Werk …" (M. Aigner, 2006, Issue 3, S. 15-16)
From the Back Cover
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.
About the Author
Alexander Schrijver is one of the most respected researchers in this area. He 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".
Most helpful customer reviews
3 of 3 people found the following review helpful.
The best book on the topic
By Arash Saber Tehrani
if u do research on combinatorial optimization like i do then this is the best book to read! Although it is not the easiest book out there but the three volumes work as a great encyclopedia on the subject! I specially like the second volume on matroids and submodular functions!
1 of 1 people found the following review helpful.
The Bible!
By Rodolfo A. Carvajal
This is a great set of books. Just two things to keep in mind:
- Its main objective is to cover a *polyhedral* approach to Combinatorial Optimization.
- Since is mean to be more of a reference book, some proofs or arguments are not explained in a lot of detail. You have to think a lot while reading... which is good.
21 of 22 people found the following review helpful.
A encyclopaedic reference on combinatorial optimization
By Mohit Tawarmalani
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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