The Art of Computer Programming, Volume 4A

Combinatorial Algorithms

Author: Donald E. Knuth

Publisher: Addison-Wesley Professional

ISBN: 0133488853

Category: Computers

Page: 912

View: 6014

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The Art of Computer Programming, Volume 4A: 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 be: “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 anew: 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. The Art of Computer Programming, Volumes 1-4A Boxed Set, 3/e ISBN: 0321751043
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Art of Computer Programming, Volume 4, Fascicle 4,The

Generating All Trees--History of Combinatorial Generation

Author: Donald E. Knuth

Publisher: Addison-Wesley Professional

ISBN: 0132702347

Category: Computers

Page: 128

View: 5194

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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. The Art of Computer Programming, Volumes 1-4A Boxed Set, 3/e ISBN: 0321751043 Art of Computer Programming, Volume 4, Fascicle 4,The: Generating All Trees--History of Combinatorial Generation: Generating All Trees--History of Combinatorial Generation 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 4 This latest fascicle covers the generation of all trees, a basic topic that has surprisingly rich ties to the first three volumes of The Art of Computer Programming. In thoroughly discussing this well-known subject, while providing 124 new exercises, Knuth continues to build a firm foundation for programming. To that same end, this fascicle also covers the history of combinatorial generation. Spanning many centuries, across many parts of the world, Knuth tells a fascinating story of interest and relevance to every artful programmer, much of it never before told. The story even includes a touch of suspense: two problems that no one has yet been able to solve.
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An Introduction to the Analysis of Algorithms

Introdu Analysi Algori_p2

Author: Robert Sedgewick,Philippe Flajolet

Publisher: Addison-Wesley

ISBN: 0133373487

Category: Computers

Page: 604

View: 9956

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Despite growing interest, basic information on methods and models for mathematically analyzing algorithms has rarely been directly accessible to practitioners, researchers, or students. An Introduction to the Analysis of Algorithms, Second Edition, organizes and presents that knowledge, fully introducing primary techniques and results in the field. Robert Sedgewick and the late Philippe Flajolet have drawn from both classical mathematics and computer science, integrating discrete mathematics, elementary real analysis, combinatorics, algorithms, and data structures. They emphasize the mathematics needed to support scientific studies that can serve as the basis for predicting algorithm performance and for comparing different algorithms on the basis of performance. Techniques covered in the first half of the book include recurrences, generating functions, asymptotics, and analytic combinatorics. Structures studied in the second half of the book include permutations, trees, strings, tries, and mappings. Numerous examples are included throughout to illustrate applications to the analysis of algorithms that are playing a critical role in the evolution of our modern computational infrastructure. Improvements and additions in this new edition include Upgraded figures and code An all-new chapter introducing analytic combinatorics Simplified derivations via analytic combinatorics throughout The book’s thorough, self-contained coverage will help readers appreciate the field’s challenges, prepare them for advanced results—covered in their monograph Analytic Combinatorics and in Donald Knuth’s The Art of Computer Programming books—and provide the background they need to keep abreast of new research. "[Sedgewick and Flajolet] are not only worldwide leaders of the field, they also are masters of exposition. I am sure that every serious computer scientist will find this book rewarding in many ways." —From the Foreword by Donald E. Knuth
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Applied Discrete Structures - Part 2- Algebraic Structures

Author: Ken Levasseur,Al Doerr

Publisher: Lulu.com

ISBN: 1105618986

Category: Science

Page: 280

View: 9829

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Applied Discrete Structures, Part II - Algebraic Structures, is an introduction to groups, monoids, vector spaces, lattices, boolean algebras, rings and fields. It corresponds with the content of Discrete Structures II at UMass Lowell, which is a required course for students in Computer Science. It presumes background contained in Part I - Fundamentals. Applied Discrete Structures has been approved by the American Institute of Mathematics as part of their Open Textbook Initiative. For more information on open textbooks, visit http: //www.aimath.org/textbooks/. This version was created using Mathbook XML (https: //mathbook.pugetsound.edu/) Al Doerr is Emeritus Professor of Mathematical Sciences at UMass Lowell. His interests include abstract algebra and discrete mathematics. Ken Levasseur is a Professor of Mathematical Sciences at UMass Lowell. His interests include discrete mathematics and abstract algebra, and their implementation using computer algebra systems.
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Combinatorics: Ancient & Modern

Author: John J. Watkins,Ronald Graham

Publisher: Oxford University Press

ISBN: 0199656592

Category: Mathematics

Page: 381

View: 2277

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Combinatorics is the branch of discrete mathematics that studies (and counts) permutations, combinations, and arrangements of sets of elements. This book constitutes the first book-length survey of the history of combinatorics and uniquely assembles research in the area that would otherwise be inaccessible to the general reader.
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Art of Computer Programming, Volume 2

Seminumerical Algorithms

Author: Donald E. Knuth

Publisher: Addison-Wesley Professional

ISBN: 0321635760

Category: Computers

Page: 784

View: 1040

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The bible of all fundamental algorithms and the work that taught many of today's software developers most of what they know about computer programming. —Byte, September 1995 I can't begin to tell you how many pleasurable hours of study and recreation they have afforded me! I have pored over them in cars, restaurants, at work, at home... and even at a Little League game when my son wasn't in the line-up. —Charles Long If you think you're a really good programmer... read [Knuth's] Art of Computer Programming... You should definitely send me a resume if you can read the whole thing. —Bill Gates It's always a pleasure when a problem is hard enough that you have to get the Knuths off the shelf. I find that merely opening one has a very useful terrorizing effect on computers. —Jonathan Laventhol The second volume offers a complete introduction to the field of seminumerical algorithms, with separate chapters on random numbers and arithmetic. The book summarizes the major paradigms and basic theory of such algorithms, thereby providing a comprehensive interface between computer programming and numerical analysis. Particularly noteworthy in this third edition is Knuth's new treatment of random number generators, and his discussion of calculations with formal power series.
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