The Art of Computer Programming, Volume 4, Fascicle 0: Introduction to Combinatorial Algorithms and Boolean Functions (Paperback)

by Donald E. Knuth (Author)

Editorial Reviews

Product Description
This multivolume work on the analysis of algorithms has long been recognized as the definitive description of classical computer science. The three complete volumes published to date already comprise a unique and invaluable resource in programming theory and practice. Countless readers have spoken about the profound personal influence of Knuth’s writings. Scientists have marveled at the beauty and elegance of his analysis, while practicing programmers have successfully applied his “cookbook” solutions to their day-to-day problems. All have admired Knuth for the breadth, clarity, accuracy, and good humor found in his books.

To begin the fourth and later volumes of the set, and to update parts of the existing three, Knuth has created a series of small books called fascicles, which will be published at regular intervals. Each fascicle will encompass a section or more of wholly new or revised material. Ultimately, the content of these fascicles will be rolled up into the comprehensive, final versions of each volume, and the enormous undertaking that began in 1962 will be complete.

Volume 4, Fascicle 0

This fascicle introduces what will become by far the longest chapter in The Art of Computer Programming, a chapter on combinatorial algorithms that will itself fill three full-sized volumes. Combinatorial algorithms, informally, are techniques for the high-speed manipulation of extremely large quantities of objects, such as permutations or the elements of graphs. Combinatorial patterns or arrangements solve vast numbers of practical problems, and modern approaches to dealing with them often lead to methods that are more than a thousand times faster than the straightforward procedures of yesteryear. This fascicle primes the pump for everything that follows in the chapter, discussing first the essential ideas of combinatorics and then introducing fundamental ideas for dealing efficiently with 0s and 1s inside a machine, including Boolean basics and Boolean function evaluation. As always, the author’s exposition is enhanced by hundreds of new exercises, arranged carefully for self-instruction, together with detailed answers.



About the Author
Donald E. Knuth is known throughout the world for his pioneering work on algorithms and programming techniques, for his invention of the TeX and Metafont systems for computer typesetting, and for his prolific and influential writing. Professor Emeritus of The Art of Computer Programming at Stanford University, he currently devotes his time to the completion of these fascicles and the seven volumes to which they belong.

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Product Details

• Paperback: 240 pages
• Publisher: Addison-Wesley Professional; 1 edition (April 27, 2008)
• Language: English
• ISBN-10: 0321534964
• ISBN-13: 978-0321534965
• Product Dimensions: 9.4 x 6.4 x 0.7 inches
• Shipping Weight: 15.5 ounces (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars See all reviews (3 customer reviews)
• Amazon.com Sales Rank: #189,026 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

6 of 6 people found the following review helpful:

5.0 out of 5 stars A fresh introduction to combinatorial thinking, May 2, 2008

By	Roozbeh Pournader - See all my reviews (REAL NAME)

For those interested in combinatorial thinking, ranging from combinatorial card game puzzles to how to count the number of ways to do something, this is a great re-introduction. In this first part of the long-awaited Volume 4, Knuth tells you why he loves combinatorics and computer algorithms, and why it took him so long to publish volume 4.

Hearing it from Knuth, the fascicle basically reassured me in my personal dance with mathematics and algorithmics: there is no problem if you love these things!

I highly recommended this to few friends who were computer science students, and they really liked it. They could not stop reading it during a party at our home!

Disclaimer: This review is based on the preview version that was made available on Knuth's home page. I believe not much is changed, except that some errors should be corrected.

1 of 1 people found the following review helpful:

5.0 out of 5 stars TAOCP: Volume 4 - Fascicle 0, June 23, 2008

By	Dimitrios I. Diochnos (Chicago, IL USA) - See all my reviews (REAL NAME)

I bought this book after a class I had in "Boolean Functions" and I must admit that the content was superb. Many interesting subjects about boolean functions, an extensive range of problems with solutions, and certainly a great deal of "food for thought" for further applications or research. All in all, a highly recommended book, and I am only wondering why volume 4 is not published in its final version (assuming that the rest of fascicles are in the same form). If you are interested in the field, just buy it.

2 of 3 people found the following review helpful:

5.0 out of 5 stars the richness of Boolean functions, May 16, 2008

By	W Boudville (Terra, Sol 3) - See all my reviews (TOP 50 REVIEWER)    (REAL NAME)

Nobody should read this book lightly. It continues the decades-long practice of Knuth's series, by furnishing a huge set of exercises in the computational field. Yet ones where the emphasis is not on writing computer programs, though he does have some problems where you are asked to do this. Instead, you have to nut out puzzles in what you might term applied number theory. A key trait of the book, and of the entire series, is that the reduction of an algorithm to source code is a relatively minor aspect.

The book differs from the first 3 volumes in the surfeit of problems. Perhaps in part because decades have elapsed since those volumes came out. During which, Knuth accrued ever more problems that he now gives us.

The focus of this book on Boolean functions can be an eye opener to some readers. You might think, naively, how difficult could the theory of Boolean functions be? Knuth shows that there is a vast level of complexity and conceptual richness lurking in such apparently simple functions. The typical computer science text that mentions Boolean functions might devote some space to examples of these. But it rarely goes deeper than explaining how to optimise, say, ORs of ANDs, where this is used for in turn optimising circuit layouts on a chip. Knuth goes way beyond this.

Granted, those are introductory CS texts, and this is not. But the average computer programmer or chip designer rarely goes beyond those in mathematical depth. And so is unlikely to have seen the material in this book.