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

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Computers and Intractability: A Guide to the Theory of NP-Completeness (Series of Books in the Mathematical Sciences) ReviewAll those who deals with Computer Science,Mathematics and Engineering have to face thereality 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.Computers and Intractability: A Guide to the Theory of NP-Completeness (Series of Books in the Mathematical Sciences) Overview

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