Combinatorial Optimization: Theory and Algorithms (Algorithms and Combinatorics)

This is the most comprehensive compilation on combinatorial optiomization I have seen so far. Usually, Papadimitriou's book is a good place for this material - but in many cases, looking for proofs and theorems - I had to use several books: (*) Combinatorial Optimization Algorithms and Complexity by Papadimitriou and Steiglitz. (*) Integer and Combinatorial Optimization by Nemhauser and Wolsey (*) Theory of linear and integer programming by Schrijver (*) Combinatorial Optimization by Cook, Cunningham, Pulleyblank and Schrijver (*)Combinatorial Algorithms by Kreher and Stinson This book, on the other hand, contains so much information and so many proved theorems - it's the richest resuorce in this topic, in my humble opinion. Using it as a graduate level textbook for an *introduction* to combinatorial optimization is kind of hard - as although it's richness, some topics are described without enough detail or examples (like the topics on network flow and bipartite graphs) - yet the authors probably assumed some previous knowledge in those topics. I prefer using this book as a reference rather than and intoduction. The heavy mathematical notations in this book might scare some readers, but no-fear! You quickly get used to it, and appreciate the greatness in the notations, as they make the theorems more short and to the point. On the other hand - getting back to this book for a quick review on some subject might force you to flip pages for a fwe minutes, just to remember the notation again. The authors intended this book to be a graduaet level textbook or an up-to-date reference work for current research. I believe they accomplished both targets! This comprehensive textbook on combinatorial optimization puts special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It has arisen as the basis of several courses on combinatorial optimization and more special topics at graduate level. Since the complete book contains enough material for at least four semesters (4 hours a week), one usually selects material in a suitable way. The book contains complete but concise proofs, also for many deep results, some of which did not appear in a book before. Many very recent topics are covered as well, and many references are provided. Thus this book represents the state of the art of combinatorial optimization. This third edition contains a new chapter on facility location problems, an area which has been extremely active in the past few years. Furthermore there are several new sections and further material on various topics. New exercises and updates in the bibliography were added. From the reviews of the 2nd edition: "This book on combinatorial optimization is a beautiful example of the ideal textbook." Operations Research Letters 33 (2005), p.216-217 "The second edition (with corrections and many updates) of this very recommendable book documents the relevant knowledge on combinatorial optimization and records those problems and algorithms that define this discipline today. To read this is very stimulating for all the researchers, practitioners, and students interested in combinatorial optimization." OR News 19 (2003), p.42

This comprehensive textbook on combinatorial optimization places special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It has arisen as the basis of several courses on combinatorial optimization and more special topics at graduate level. It contains complete but concise proofs, also for many deep results, some of which did not appear in a textbook before. Many very recent topics are covered as well, and many references are provided. Thus this book represents the state of the art of combinatorial optimization.

This fourth edition is again significantly extended, most notably with new material on linear programming, the network simplex algorithm, and the max-cut problem. Many further additions and updates are included as well.

"This comprehensive textbook on combinatorial optimization puts special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It has arisen as the basis of several courses on combinatorial optimization and more special topics at graduate level. Since the complete book contains enough material for at least four semesters (4 hours a week), one usually selects material in a suitable way." "The book contains complete but concise proofs, also for many deep results, some of which did not appear in a book before. Many very recent topics are covered as well, and many references are provided. Thus this book represents the state of the art of combinatorial optimization."--Jacket