Computers and Intractability: A Guide to the Theory of NP-Completeness (Series of Books in the Mathematical Sciences) [Paperback]

M. R. Garey (Author), D. S. Johnson (Author)

Editorial Reviews

Amazon.com Review

This book's introduction features a humorous story of a man with a line of people behind him, who explains to his boss, "I can't find an efficient algorithm, but neither can all these famous people." This man illustrates an important quality of a class of problems, namely, the NP-complete problems: if you can prove that a problem is in this class, then it has no known polynomial-time solution that is guaranteed to work in general. This quality implies that the problem is difficult to deal with in practice.

The focus of this book is to teach the reader how to identify, deal with, and understand the essence of NP-complete problems; Computers and Intractability does all of those things effectively. In a readable yet mathematically rigorous manner, the book covers topics such as how to prove that a given problem is NP-complete and how to cope with NP-complete problems. (There is even a chapter on advanced topics, with numerous references.) Computers and Intractability also contains a list of more than 300 problems--most of which are known to be NP-complete--with comments and references.

Product Details

• Paperback: 340 pages
• Publisher: W. H. Freeman; First Edition edition (January 15, 1979)
• Language: English
• ISBN-10: 0716710455
• ISBN-13: 978-0716710455
• Product Dimensions: 6.6 x 0.7 x 9.2 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Average Customer Review: 4.9 out of 5 stars  See all reviews (14 customer reviews)
• Amazon Best Sellers Rank: #58,844 in Books (See Top 100 in Books)
  • #2 in Books > Computers & Technology > Programming > APIs & Operating Environments > Device Drivers
  • #72 in Books > Computers & Technology > Programming > Algorithms

Most Helpful Customer Reviews

32 of 35 people found the following review helpful

5.0 out of 5 stars Contemplating Abstract Thought April 29, 2000

By S. Wuest

Format:Paperback

Every graduate CS student will probably encounter this book--it is a classic.

But long after that course in NP theory was over, the astonishment of a different aspect of the book remains.

One course assignment was the development of 15 polynomial reduction proofs (proving the computational complexity equivalence of pairs of NP problems). Part of these proofs can be simple geometric shapes, locations and connecting lines, which are defined as elements in the 2 problems. Because the elements are rigorously defined, the resulting geometric pictures model rigorous proofs of equivalence.

I was astounded at the power of such abstractions (which most programmers perhaps wouldn't even recognize as legitimate proofs). This experience underlined the fact that rigorous logical proof may take many outer forms, whether mathematical equations, formal symbolic logic proofs such as the Irving Copi notation, or simple geometric drawings.

Many veins of rich ore may be mined from this work, and only 1 of them is NP theory. But the reader must be ready to do battle with some difficult ideas, and mathematical notation which can obscure the creativity of the material covered. (For astounding creativity, examine Cooke's Theorem proving that the Satisfiability problem is NP-Complete!)

22 of 23 people found the following review helpful

5.0 out of 5 stars On the difficulty of computers to deal with certain problems April 16, 1997

By A Customer

Format:Paperback

All those who deals with Computer Science,
Mathematics and Engineering have to face the
reality that certain problems seem really hard
to solve. Even with the more sophisticated, and
technologically advanced among the currently
available computers---and among those that are to
come in the next several years---, it seems highly
likely that we cannot efficiently solve certain
specific problems.

A first well written and systematic account on
the hardness of this problems is the 1979 book on
the theory of NP completeness by Michael R. Garey
and David S. Johnson: Computers and
Intractability, A Guide to the Theory of
NP-Completeness (W.H. Freeman and Company, San
Francisco). It is amazing how, after all these
years, this book remains a fundamental one to be
introduced on what can be effectively and
efficiently solved by computers and above all on
what it seems not efficiently solvable,
independently of the advances of technology.
Other texts have been published after that one,
as for example the recent clear and complete
overview on what has been done and extensively
researched since then that has been given by
Christos H. Papadimitriou in his book
Computational Complexity (Addison-Wesley, 1994).
Nevertheless, the Garey-Johnson book---as it is
often familiarly called---remains the fundamental
book for a clear introduction to this central
problem of what is tractable by computers.

Starting from a very clear introduction to the
technical term "NP-Complete," and to how this
term gained importance for the description of the
algorithmic tractability of certain problems in
the early 70s, the book clearly defines, both in
an intuitive and then in a formal way, what it is
meant by the complexity of a problem. More than
that, this complexity is directly related to the
effective methods for solving problems
(algorithms) and thus to computers themselves.
The basic of the theory of NP-Completeness is
completely covered in the first 5 chapters,
beginning from a low-level introduction to some
of the central notions of computational
complexity and finally providing detailed
definitions describing proof techniques to prove
the hardness of certain problems. The remaining
two chapters provide an overview on two
alternative directions for further study. (The
both of them have been extensively investigated
in the following years.) Finally, the appendix
contains more than 300 main entries on
NP-Complete and NP-Hard problems, and this last
part of the book is continuously referenced in
journal and conference papers on the subject.

The first chapter is definitely accessible also
to those that doesn't know so much mathematics,
or computers related stuff, and thus the book is
recommendable to those that are simply curious
about the things that can be solved with
computers.

11 of 12 people found the following review helpful

5.0 out of 5 stars A classic! September 14, 2000

By Todd Ebert

Format:Paperback

I think every computer science student should read some of this book to learn about complexity theory and the notions reducibilty and completeness. Moreover, you may come across a problem that you have to show is NP or P complete, and the examples in the book provide a good model for doing so. Papadimitriou's book on complexity is also a great place to learn more about the subject.