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.
As in every volume of this remarkable series, the book includes hundreds of exercises that employ Knuth's ingenious rating system, making it easy for readers of varying degrees of mathematical training to find challenges suitable to them. Detailed answers are provided to facilitate self-study.
Professor Donald E. Knuth has always loved to solve problems. In Volume 4B he now promotes two brand new and practical general problem solvers, namely (0) the Dancing Links Backtracking and (1) the SAT Solver. To use them, a problem is defined declaratively (0) as a set of options, or (1) in Boolean formulae. Today's laptop computers, heavily armoured with very high speed processors and ultra large amounts of memory, are able to run either solver for problems having big input data. Each section of Volume 4B contains a multitudinous number of tough exercises which help make understanding surer. Happy reading! -- Eiiti Wada, an elder computer scientist, UTokyo
Donald Knuth may very well be a great master of the analysis of algorithms, but more than that, he is an incredible and tireless storyteller who always strikes the perfect balance between theory, practice, and fun. [ Volume 4B, Combinatorial Algorithms, Part 2 ] dives deep into the fascinating exploration of search spaces (which is quite like looking for a needle in a haystack or, even harder, to prove the absence of a needle in a haystack), where actions performed while moving forward must be meticulously undone when backtracking. It introduces us to the beauty of dancing links for removing and restoring the cells of a matrix in a dance which is both simple to implement and very efficient. --Christine Solnon, Department of Computer Science, INSA Lyon
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The art of computer programming, volume 4b,: combinatorial algorithms

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

Knuth, Donald E.

Addison Wesley Professional

Da Capo Press, Incorporated

Pearson Education, Limited

Hachette Books

Basic Books

United States, United States of America

Pearson Education (US), Hoboken, 2022

Reading, Mass, ©1997-<2022>

2019

2020

Publisher's PDF | Published by Addison-Wesley Professional (September 28, 2022) | NOTE!: 2nd Printing, November 2022

Cover
Half Title
Title Page
Copyright Page
Contents
Preface
Notes on the Exercises
Mathematical Preliminaries Redux
Inequalities
Martingales
Tail inequalities from martingales
Applications
Statements that are almost sure, or even quite sure
Exercises
Chapter 7—Combinatorial Searching
7.2. Generating All Possibilities
7.2.1. Generating Basic Combinatorial Patterns
7.2.2. Backtrack Programming
Data structures
Walker’s method
Permutations and Langford pairs
Word rectangles
Commafree codes
Dynamic ordering of choices
Sequential allocation redux
Lists for the commafree problem
A general mechanism for doing and undoing
Backtracking through commafree codes
Running time estimates
Estimating the number of solutions
Factoring the problem
Historical notes
Exercises
7.2.2.1. Dancing links
Exact cover problems
Secondary items
Progress reports
Sudoku
Polyominoes
Polycubes
Factoring an exact cover problem
Color-controlled covering
Introducing multiplicity
A new dance step
Analysis of Algorithm X
Analysis of matching problems
Maintaining a decent focus
Exploiting local equivalence
Preprocessing the options
Minimum-cost solutions
Implementing the min-cost cutoffs
Dancing with ZDDs
Summary
Historical notes
Exercises—First set
Exercises—Second set
Exercises—Third set
7.2.2.2. Satisfiability
Example applications
Backtracking algorithms
Random clauses
Resolution of clauses
Clause-learning algorithms
Monte Carlo algorithms
The Local Lemma
Message-passing algorithms
Preprocessing of clauses
Encoding constraints into clauses
Unit propagation and forcing
Symmetry breaking
Satisfiability-preserving maps
One hundred test cases
Tuning the parameters
Exploiting parallelism
History
Exercises
Answers to Exercises
Appendix A—Tables of Numerical Quantities
1. Fundamental Constants (decimal
2. Fundamental Constants (hexadecimal)
3. Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers
Appendix B—Index to Notations
Appendix C—Index to Algorithms and Theorems
Appendix D—Index to Combinatorial Problems
Appendix E—Answers to Puzzles in the Answers
Index and Glossary
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z

This first volume begins with basic programming concepts and techniques, then focuses on information structures--the representation of information inside a computer, the structural relationships between data elements and how to deal with them efficiently. Elementary applications are given to simulation, numerical methods, symbolic computing, software and system design

2024-02-18