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Title: Combinatorial Optimization: Algorithms and Complexity by Christos H. Papadimitriou, Kenneth Steiglitz ISBN: 0-486-40258-4 Publisher: Dover Publications Pub. Date: 01 June, 1998 Format: Paperback Volumes: 1 List Price(USD): $18.95

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Average Customer Rating: 4.86 (7 reviews)

Rating: 5
Summary: It is the Globally Optimal Solution!
Comment: I can't say more than what already been said by other reviewers. To recap,

F = {all excellent combinatorial optimization books}
cost(this_book) <= cost(y) for all y in F.

;)

Rating: 5
Summary: Inexpensive, excellently written, and quite interesting!
Comment: I had this book on my shelf for two years before taking a serious look at it, and only wish I had read it much earlier in life. Christos Papadimitriou has written quite a gem! On one hand this book serves as a good introduction to combinatorial optimization algorithms, in that it provides a flawless introduction to the simplex algorithm, linear and integer programming, and search techniques such as Branch-and-Bound and dynamic programming. On another, it serves as a good reference for many graph-theoretic algorithms. But most importantly Papadimitriou and Steiglitz seem to be on a quest to understand why some problems, such as Minimum Path or Matching, have efficient solutions, while others, such as Traveling Salesman, do not. And in doing so they end up providing the reader with a big picture behind algorithms and complexity, and the connection between optimization problems and complexity.

After reading this and Papadimitriou's "Introduction to Computational Complexity" (which I also highly recommend), I now consider him one of the best at conveying complex ideas in a way that rarely confuses the reader. I also had the priviledge of attending one of his talks on complexity, and he seems just as effusive and transparent as a lecturer as he does a writer. Ah, for once I bought a Dover book that did not disappoint.

Rating: 5
Summary: It worths exponentially much more than its price
Comment: One could buy this book for different reasons: interests in combinatorial optimization, of course; interests in what Papadimitriou has to say, since his thoughts on this subject are definitely invaluable; perhaps the price is a good reason alone.
Whatever the reason, however, I think that would be a rare event to remain duped.

I was preparing my exam in Computability and Complexity when I first used it. I've been wonderfully surprised by the amount of definitions, algorithms, concepts I've found in this book. I think one could use this book for a simple course on Algorithms, on Computability and/or Complexity, on the whole Combinatorial Optimization, and the book would be always and costantly useful.

The chapters on algorithms and complexity, or those on NP completeness have proved to be gems. The chapters on Approximation and Local Search are great, and they feature a bunch of detailed and excellent quality stuff (e.g. there is a detailed treatment of Christofides' algorithm to approximate the TSP, that is quite an idiosyncratic topic).

All in all, a very great book, with a value exponentially greater than the very insignificant price.

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