Art of Computer Programming, The: Combinatorial Algorithms, Volume 4B

The Art of Computer Programming is Knuth’s multivolume analysis of algorithms. With the addition of this new volume, it continues to be the definitive description of classical computer science.

Volume 4B, the sequel to Volume 4A, extends Knuth’s exploration of combinatorial algorithms. These algorithms are of keen interest to software designers because “. . . a single good idea can save years or even centuries of computer time.”

The book begins with coverage of Backtrack Programming, together with a set of data structures whose links perform “delightful dances” and are ideally suited to this domain. New techniques for important applications such as optimum partitioning and layout are thereby developed.

Knuth’s writing is playful, and he includes dozens of puzzles to illustrate the algorithms and techniques, ranging from popular classics like edge-matching to more recent crazes like sudoku. Recreational mathematicians and computer scientists will not be disappointed!

In the second half of the book, Knuth addresses Satisfiability, one of the most fundamental problems in all of computer science. Innovative techniques developed at the beginning of the twenty-first century have led to game-changing applications, for such things as optimum scheduling, circuit design, and hardware verification. Thanks to these tools, computers are able to solve practical problems involving millions of variables that only a few years ago were regarded as hopeless.

The Mathematical Preliminaries Redux section of the book is a special treat, which presents basic techniques of probability theory that have become prominent since the original “preliminaries” were discussed in Volume 1.

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