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Approximation Algorithms [Hardcover]

by Vijay V. Vazirani
5.0 out of 5 stars  See all reviews (9 customer reviews)

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Book Description

December 5, 2002 3540653678 978-3540653677
Covering the basic techniques used in the latest research work, the author consolidates progress made so far, including some very recent and promising results, and conveys the beauty and excitement of work in the field. He gives clear, lucid explanations of key results and ideas, with intuitive proofs, and provides critical examples and numerous illustrations to help elucidate the algorithms. Many of the results presented have been simplified and new insights provided. Of interest to theoretical computer scientists, operations researchers, and discrete mathematicians.

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Editorial Reviews


From the reviews:

"Approximation algorithms is an area where much progress has been made in the last 10 years. The book under review is a very good help for understanding these results. In each of the 27 chapters an important combinatorial optimization problem is presented and one or more approximation algorithms for it are clearly and concisely described and analyzed. In this way most of the most important results from the approximation algorithm literature are covered, often more easily comprehensible than the original articles." (Viggo Kann, Zentralblatt MATH, Vol. 1005, 2003)

"The book under review concentrates on the … design and analysis of efficient approximation algorithms with good performance guarantees. It is possibly the first textbook to provide an extensive and systematic coverage of this topic. … The book starts briskly, using simple examples to illustrate some of the key concepts and draw the reader rapidly in. … Copious exercises are included to test and deepen the reader’s understanding. … It deserves a place in every computer science and mathematical library." (Mark R. Jerrum, Mathematical Reviews, 2002 h)

"The book of Vijay Vazirani is not the first one dedicated to approximation algorithms … . However it is, I believe, among the very best from a didactical point of view: this is the text I would chose, would I have to give a course on approximation algorithms … . I suspect that for many researchers it would be the first one to consult … . It is a must acquisition for libraries of computer science/engineering departments … ." (Francesco Maffioli, Mathematical Methods of Operations Research, Vol. 56 (2), 2002)

"The book gives an overview on the theory of approximation algorithms. It presents the most important problems, the basic methods and ideas which are used in this area. … The book can be used for a graduate course on approximation algorithms. … The chapters also contain a section of exercises, which can help the students to understand the material in a deeper way. … On the other hand the book can be used by the researchers of the field … ." (Csanád Imreh, Acta Scientiarum Mathematicarum, Vol. 68, 2002)

From the Back Cover

 This book covers the dominant theoretical approaches to the approximate solution of hard combinatorial optimization and enumeration problems. It contains elegant combinatorial theory, useful and interesting algorithms, and deep results about the intrinsic complexity of combinatorial problems. Its clarity of exposition and excellent selection of exercises will make it accessible and appealing to all those with a taste for mathematics and algorithms.

Richard Karp,University Professor, University of California at Berkeley

Following the development of basic combinatorial optimization techniques in the 1960s and 1970s, a main open question was to develop a theory of approximation algorithms. In the 1990s, parallel developments in techniques for designing approximation algorithms as well as methods for proving hardness of approximation results have led to a beautiful theory. The need to solve truly large instances of computationally hard problems, such as those arising from the Internet or the human genome project, has also increased interest in this theory. The field is currently very active, with the toolbox of approximation algorithm design techniques getting always richer.

It is a pleasure to recommend Vijay Vazirani's well-written and comprehensive book on this important and timely topic. I am sure the reader will find it most useful both as an introduction to approximability as well as a reference to the many aspects of approximation algorithms.

László Lovász, Senior Researcher, Microsoft Research

Product Details

  • Hardcover: 380 pages
  • Publisher: Springer (December 5, 2002)
  • Language: English
  • ISBN-10: 3540653678
  • ISBN-13: 978-3540653677
  • Product Dimensions: 9.6 x 6.4 x 1.1 inches
  • Shipping Weight: 1.6 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (9 customer reviews)
  • Amazon Best Sellers Rank: #473,286 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
51 of 51 people found the following review helpful
5.0 out of 5 stars No approximations, this is THE optimal book! February 16, 2002
I have been using Dorit Hochbaum's book on approximation algorithms for NP-Hard problems as a guideline for my work. Hochbaum's book is, without a doubt, terrific. However, the survey format compromised a smooth flow in favor of bringing together the best people in the field. This book (Vazirani's) corrects this by being so smooth and elegant from start to finish. Excellent problem sets, excellent hints for most problems, and there is a section at the end of the book devoted to open problems, which is a really really cool feature. My favorite chapter -29 I think- deals with hardness of approximation and the PCP theorem. The chapter explains the PCP theorem so vividly that the exact next thing I was doing was reading and comprehending the latest papers in this area. If you're a researcher in algorithms and complexity, then this book is highly recommended, especially at this ridiculously low price.
Note on my background: I am a graduate (masters) student in CS.
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7 of 7 people found the following review helpful
5.0 out of 5 stars Very nice introduction May 19, 2006
This is a quite nice book by an author who is well-known in the field. The book is not thematic, instead it presents certain problems in each chapter along with the main approximation algorithms and correctness proofs. Yet, each new concept is well introduced with the problems. For instance, the author presents LP-based techniques on the same problem (set cover) in the second part of the book. This makes it quite easy to compare and understand different techniques. The last part of the book is a little bit advanced compared to the first two parts which uses combinatorial or LP-based analysis of the algorithms. The presentation of the PCP theorem- arguably the deepest theorem of computer science- and its consequences are also in the last part.

A warning though: The book is quite terse at times, which enforces a dense reading. This may not be suitable for an undergradute study. My only complaint is that the PCP theorem might well be introduced with a little more intution.

Overall, I rate this book as excellent. If you are interested in algorithms, you should definitely buy it. Also, buy the "Complexity and Approximation" by Ausiello, Crescenzi and others. They provide a more comprehensive and thematic treatment. It also has an excellent bibliography and list of NP-hard problems. These two will make a great couple. The book edited by Hochbaum (Approximation Algorithms for NP-hard problems) on the other hand presents detailed information on the algorithms.
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7 of 7 people found the following review helpful
I have been looking for books related to solving NP-complete and NP-hard problems approximately. There is another book by Hochbaum and I have that too. Unfortunately, that book is more of a research oriented book as it is written by several researchers. It's like reading several research papers within two hard covers. This means that one needs to have a sort of intermediate level of experience with approximation algorithms.

For a beginner, one would expect a book that starts from ground-up and that has been written as a textbook rather than as a set of research papers. The book by Dr. Vazirani, is the only book that is written by one author with a step-by-step evolution of concepts and ideas related to approximation algorithms.
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3 of 3 people found the following review helpful
5.0 out of 5 stars a favorite December 8, 2011
By Vivace
This is not only the best Appoximation Algorithm book out there, its one of the best books on graduate level mathematics I have ever seen. Such eloquent coverage of advanced topics. I can not recommend it highly enough.
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2 of 2 people found the following review helpful
5.0 out of 5 stars A way in to deeper optimization algorithms June 3, 2010
I have always been a operational research aficionado, but when I skimmed through this book the first time I did not really "get it". Then, I was led back to this book and now it has become one of those books I like to pick up just to bring the remembrance of the concepts it talks about. One main topic is duality and how for different problems we can squeeze the gap between the solution built in primal and dual space. I have known the theory for years, yet it is only more recently and with help among others from this book, that I start to get a glimpse of the whole depth and magic in this area of "applied" mathematics.
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