Art of Computer Programming, The: Combinatorial Algorithms, Volume 4A, Part 1

Art of Computer Programming

by Donald Ervin Knuth

The Art of Computer Programming, Volume 4 Combinatorial Algorithms, Part 1 Knuth’s multivolume analysis of algorithms is widely recognized as the definitive description of classical computer science. The first three volumes of this work have long comprised a unique and invaluable resource in programming theory and practice. Scientists have marveled at the beauty and elegance of Knuth’s analysis, while practicing programmers have successfully applied his “cookbook” solutions to their day-to-day problems. The level of these first three volumes has remained so high, and they have displayed so wide and deep a familiarity with the art of computer programming, that a sufficient “review” of future volumes could almost “Knuth, Volume n has been published.” – Data Processing Digest Knuth, Volume n has been published, where n = 4A. In this long-awaited new volume, the old master turns his attention to some of his favorite topics in broadword computation and combinatorial generation (exhaustively listing fundamental combinatorial objects, such as permutations, partitions, and trees), as well as his more recent interests, such as binary decision diagrams. The hallmark qualities that distinguish his previous volumes are manifest here detailed coverage of the basics, illustrated with well-chosen examples; occasional forays into more esoteric topics and problems at the frontiers of research; impeccable writing peppered with occasional bits of humor; extensive collections of exercises, all with solutions or helpful hints; a careful attention to history; implementations of many of the algorithms in his classic step-by-step form. There is an amazing amount of information on each page. Knuth has obviously thought long and hard about which topics and results are most central and important, and then, what are the most intuitive and succinct ways of presenting that material. Since the areas that he covers in this volume have exploded since he first envisioned writing about them, it is wonderful how he has managed to provide such thorough treatment in so few pages . –Frank Ruskey, Department of Computer Science, University of Victoria The book is Volume 4A, because Volume 4 has itself become a multivolume undertaking. Combinatorial searching is a rich and important topic, and Knuth has too much to say about it that is new, interesting, and useful to fit into a single volume, or two, or maybe even three. This book alone includes approximately 1500 exercises, with answers for self-study, plus hundreds of useful facts that cannot be found in any other publication. Volume 4A surely belongs beside the first three volumes of this classic work in every serious programmer’s library. Finally, after a wait of more than thirty-five years, the first part of Volume 4 is at last ready for publication. Check out the boxed set that brings together Volumes 1 - 4A in one elegant case, and offers the purchaser a $50 discount off the price of buying the four volumes individually. Ebook (PDF version) produced by Mathematical Sciences Publishers (MSP), The Art of Computer Programming, Volumes 1-4A Boxed Set, 3/e 0321751043

Genres: Computer Science, Programming, Algorithms, Reference, Computers, Technology, Nonfiction

912 pages, Hardcover

First published January 22, 2011

About the author

Donald Ervin Knuth, born January 10th 1938, is a renowned computer scientist and Professor Emeritus of the Art of Computer Programming at Stanford University.

Author of the seminal multi-volume work The Art of Computer Programming ("TAOCP"), Knuth has been called the "father" of the analysis of algorithms, contributing to the development of, and systematizing formal mathematical techniques for, the rigorous analysis of the computational complexity of algorithms, and in the process popularizing asymptotic notation.

In addition to fundamental contributions in several branches of theoretical computer science, Knuth is the creator of the TeX computer typesetting system, the related METAFONT font definition language and rendering system, and the Computer Modern family of typefaces.

A prolific writer and scholar, Knuth created the WEB/CWEB computer programming systems designed to encourage and facilitate literate programming, and designed the MMIX instruction set architecture.

Reviews

[Parsa · Rating 5 out of 5]

I sort of happened to read like the first half of this volume for my job and it has a really nice exposition on everything you've ever wanted to know about boolean functions and "bitwise tricks and techniques". I can't ever hope to finish this. The exercises can go very very deep. For example, he gives a new algorithm for hypergraph transversals as a solution to exercise 237 on the BDD section, but since it was buried in the problems no one seems to have noticed it. I've spent the past 3 months working on the same problem.

Volume 4a also has some really good looking figures.

Also, I don't see why a lot of people are put off by the use of an assembly language. We learnt basic MMIX in our intro to CS class in like, one hour, and it's not even used all that much in the book.

[Nick Black]

it has finally arrived! oh, it's beautiful!
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!!!!!!!! excitement!!!!!!!!! just preordered my copy!

as a client in good standing of the Bank of San Serriffe, how could I do otherwise? http://www-cs-faculty.stanford.edu/~u... :D

[Chris]

This book will take me a _long_ time to finish, as I intend to do all exercises < 30 in difficulty.

[marcel · Rating 5 out of 5]

Unlike the other three volumes, which contain two chapter each, Volume 4A doesn't even cover a whole chapter. The reason for this is that when Knuth sketched out the skeleton of his books in the 1960s, the subject of Chapter 7, combinatorial searching, was a rather small subject. But all of that changed in the 1970s and 1980s, when the field of combinatorial algorithms exploded. The result is that Knuth took nearly forty years to write just two sections of Chapter 7, but these two sections fill more pages than any of the other three books. The first half of this volume deals with boolean functions, while the second half deals with the daunting task of enumerating all elements of some combinatorial structure (e.g., tuples, partitions, trees). I found the math in this volume to be harder than in the previous three, but I am happy that (in this volume as well as the others) Knuth is always willing to pause the flow of a section to dive into the mathematical theory. For example, in the section on set partitions, Knuth gives a detailed description of the saddle-point method of deriving asymptotics. Where this volume possibly suffers is in its breadth. The other three books all offer enough variation so that, even if you might not be interested in one particular section, you might really enjoy a different one. But with 200+ pages on boolean functions and 200+ pages on enumeration techniques, Volume 4 definitely feels a lot more laser-focused in its subject matter.

[Herman Schmit · Rating 3 out of 5]

I remember Knuth's books as too dense for me when I was younger. I thought maybe I was smarter now. Nope. They are still too dense for me.

[Manoj Khatri · Rating 5 out of 5]

Can spend my whole life just looking at the exercises.