Combinatorial Optimization: Polyhedra and Efficiency: v.24/A (Algorithms and Combinatorics)

Schrijver, Alexander

ISBN 10: 3540204563 ISBN 13: 9783540204565

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 2004

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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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)

Synopsis

From the reviews: Schrijver's 3 volumes on combinatorial optimization reflect the current state of the art in this field, in particular from the viewpoint of polyhedral combinatorics and efficient algorithms. The book offers a masterly introduction with many interesting historical remarks as well as an in-depth survey of combinatorial optimization. It is divided into eight main parts with 83 chapters. The main parts are: paths and flows; bipartite matching and covering; nonbipartite matching and covering; matroids and submodular functions; trees, branchings and connectors; cliques, stable sets and colouring; multiflows and disjoint paths and, finally; and hypergraphs. The reader is supposed to have a basic knowledge of graph theory and linear as well as integer programming. The author gives short and elegant proofs to all main results. These three volumes contain an immense richness of results up to 2002 and will prove to be indispensible for any further research in the field of combinatorial optimization.Rainer E. Burkard (Graz) Zentralblatt Math Database, 2003.

Now comes Schrijver's book, a current and extremely comprehensive account, running 1,451 pages; by itself the bibliography would make a long book. But even as the book provides reference material to satisfy the experts, strong undergraduates will profit by dipping straight into nearly any chapter. Mathematics and computer science students should consult it, both to supplement their theoretical coursework or to find algorithms for practical projects. Summing Up: All three books are recommended for Upper-division undergraduates through faculty. American Library Association, 2003.

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