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The Art of Computer Programming, Volume 4, Fascicle 0: Introduction to Combinatorial Algorithms and Boolean Functions Paperback – April 27, 2008

9 customer reviews
ISBN-13: 978-0321534965 ISBN-10: 0321534964 Edition: 1st

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The Art of Computer Programming, Volume 4, Fascicle 0: Introduction to Combinatorial Algorithms and Boolean Functions + The Art of Computer Programming, Volume 4, Fascicle 1: Bitwise Tricks & Techniques; Binary Decision Diagrams + The Art of Computer Programming, Volume 4, Fascicle 2: Generating All Tuples and Permutations
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Editorial Reviews

From the Back Cover

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 calledfascicles, 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 inThe 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: 6.3 x 0.7 x 9.5 inches
  • Shipping Weight: 15.5 ounces (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (9 customer reviews)
  • Amazon Best Sellers Rank: #971,568 in Books (See Top 100 in Books)

More About the Author

Donald E. Knuth was born on January 10, 1938 in Milwaukee, Wisconsin. He studied mathematics as an undergraduate at Case Institute of Technology, where he also wrote software at the Computing Center. The Case faculty took the unprecedented step of awarding him a Master's degree together with the B.S. he received in 1960. After graduate studies at California Institute of Technology, he received a Ph.D. in Mathematics in 1963 and then remained on the mathematics faculty. Throughout this period he continued to be involved with software development, serving as consultant to Burroughs Corporation from 1960-1968 and as editor of Programming Languages for ACM publications from 1964-1967.

He joined Stanford University as Professor of Computer Science in 1968, and was appointed to Stanford's first endowed chair in computer science nine years later. As a university professor he introduced a variety of new courses into the curriculum, notably Data Structures and Concrete Mathematics. In 1993 he became Professor Emeritus of The Art of Computer Programming. He has supervised the dissertations of 28 students.

Knuth began in 1962 to prepare textbooks about programming techniques, and this work evolved into a projected seven-volume series entitled The Art of Computer Programming. Volumes 1-3 first appeared in 1968, 1969, and 1973. Having revised these three in 1997, he is now working full time on the remaining volumes. Volume 4A appeared at the beginning of 2011. More than one million copies have already been printed, including translations into ten languages.

He took ten years off from that project to work on digital typography, developing the TeX system for document preparation and the METAFONT system for alphabet design. Noteworthy by-products of those activities were the WEB and CWEB languages for structured documentation, and the accompanying methodology of Literate Programming. TeX is now used to produce most of the world's scientific literature in physics and mathematics.

His research papers have been instrumental in establishing several subareas of computer science and software engineering: LR(k) parsing; attribute grammars; the Knuth-Bendix algorithm for axiomatic reasoning; empirical studies of user programs and profiles; analysis of algorithms. In general, his works have been directed towards the search for a proper balance between theory and practice.

Professor Knuth received the ACM Turing Award in 1974 and became a Fellow of the British Computer Society in 1980, an Honorary Member of the IEEE in 1982. He is a member of the American Academy of Arts and Sciences, the National Academy of Sciences, and the National Academy of Engineering; he is also a foreign associate of l'Academie des Sciences (Paris), Det Norske Videnskaps-Akademi (Oslo), Bayerische Akademie der Wissenschaften (Munich), the Royal Society (London), and Rossiiskaya Akademia Nauk (Moscow). He holds five patents and has published approximately 160 papers in addition to his 28 books. He received the Medal of Science from President Carter in 1979, the American Mathematical Society's Steele Prize for expository writing in 1986, the New York Academy of Sciences Award in 1987, the J.D. Warnier Prize for software methodology in 1989, the Adelskøld Medal from the Swedish Academy of Sciences in 1994, the Harvey Prize from the Technion in 1995, and the Kyoto Prize for advanced technology in 1996. He was a charter recipient of the IEEE Computer Pioneer Award in 1982, after having received the IEEE Computer Society's W. Wallace McDowell Award in 1980; he received the IEEE's John von Neumann Medal in 1995. He holds honorary doctorates from Oxford University, the University of Paris, St. Petersburg University, and more than a dozen colleges and universities in America.

Professor Knuth lives on the Stanford campus with his wife, Jill. They have two children, John and Jennifer. Music is his main avocation.

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7 of 7 people found the following review helpful By Roozbeh Pournader on May 2, 2008
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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.
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6 of 6 people found the following review helpful By W Boudville HALL OF FAMETOP 1000 REVIEWERVINE VOICE on May 16, 2008
Format: Paperback
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.
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1 of 1 people found the following review helpful By dimis on June 23, 2008
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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.
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You might be wondering if the fascicle series is still worth getting, given the whole series has now been updated in a single text here: The Art of Computer Programming, Volume 4A: Combinatorial Algorithms, Part 1.

The answer is: it depends on whether you have a specific area of combinatorics you're interested in (example: Fascicle 0 is great for logic gates and hence circuit designers), or if you're interested in the entire area of combinatorics and all 5 fascicles (0-4).

All 5 are essentially covered in the 2011 book above, with some corrections and deletions. Don't be fooled by the "part 1" because this series can be confusing. Go to Dr. Knuth's website to see the entire map of current and planned volumes and editions, including this series in .pdf: just Google/Bing Knuth website art of programming and click on the dot cs dot faculty dot stanford link for the series.

As you'll see on the site, part 1 (if the Dr's health holds out) has now been expanded with additional draft fascicles, especially in the essentially uncovered area of stochastic combinatorics. Probability wasn't even applied to computational combinatorics yet in the 60's, so this is not a flaw in Doc Knuth's coverage! There is a 4B, 4C, 4D etc. planned, mostly expanding recursion, statistics and other new areas of combinatorics.

Great self study intro to everything computational complexity, as combinatorics greatly pushes the "big O" computing envelope, and the talented Doc Knuth even weighs in on P/NP. Many examples given with mem counts that are up to date.
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1 of 1 people found the following review helpful By Davi on January 5, 2013
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Knuth swims in Math and computer logic much as a fish does in water. Enter his mind, and you will become a legendary computer scientist, just like him.
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