Average Case Analysis of Algorithms on Sequences (Wiley Series in Discrete Mathematics and Optimization) [Hardcover]

Wojciech Szpankowski (Author)

Book Description

ISBN-10: 047124063X | ISBN-13: 978-0471240631 | Publication Date: April 16, 2001 | Edition: 1

A timely book on a topic that has witnessed a surge of interest over the last decade, owing in part to several novel applications, most notably in data compression and computational molecular biology. It describes methods employed in average case analysis of algorithms, combining both analytical and probabilistic tools in a single volume.
* Tools are illustrated through problems on words with applications to molecular biology, data compression, security, and pattern matching.
* Includes chapters on algorithms and data structures on words, probabilistic and analytical models, inclusion-exclusion principles, first and second moment methods, subadditive ergodic theorem and large deviations, elements of information theory, generating functions, complex asymptotic methods, Mellin transform and its applications, and analytic poissonization and depoissonization.
* Written by an established researcher with a strong international reputation in the field.

Editorial Reviews

Review

"Surveying the major techniques of average case analysis, this graduate textbook presents both analytical methods used for well-structured algorithms and probabilistic methods used for more structurally complex algorithms." (SciTech Book News, Vol. 25, No. 3, September 2001)

"...contains a comprehensive treatment on probabilistic, combinatorial, and analytical techniques and methods...treatment is clear, rigorous, self-contained, with many examples and exercises." (Zentralblatt MATH Vol. 968, 2001/18)

"This well-organized book...is certainly useful...It is a valuable source for a deeper and more precise understanding of the behaviors of algorithms on sequences." (Mathematical Reviews, 2002f)

From the Back Cover

Comprehensive presentation of both analytic and probabilistic techniques

As a comprehensive survey of the major techniques of average case analysis, this work presents, in detail, both analytic methods used for well-structured algorithms and probabilistic methods used for more structurally complex algorithms. In particular, the applications in the book use algorithms that focus on data structures on sequences, also called strings, which are widely used in computer science, computational biology, and information theory. Specific techniques covered include the inclusion-exclusion principle, the first and second moment methods, the random coding technique, the subadditive ergodic theorem, large deviations, generating functions, complex asymptotic methods, the Mellin transform, and analytic poissonization and depoissonization. Each method is clearly explained and accompanied by related applications and problems involving algorithms on sequences.

Important features of the book include:
* A foreword by well-known expert Dr. Philippe Flajolet, INRIA, France
* Presentation of complex analysis used to solve discrete and probabilistic problems on sequences
* Discussions of Lempel-Ziv data compression-schemes, the string edit problem, pattern matching algorithms, many variations of digital trees, the leader election algorithm, and more
* A chapter devoted to tools used in information theory, particularly the random coding technique and pattern matching approach to data compression
* Application sections in each chapter that illustrate the methods covered
* An extensive bibliography

See all Editorial Reviews

Product Details

• Hardcover: 576 pages
• Publisher: Wiley-Interscience; 1 edition (April 16, 2001)
• Language: English
• ISBN-10: 047124063X
• ISBN-13: 978-0471240631
• Product Dimensions: 9.6 x 6.4 x 1.2 inches
• Shipping Weight: 2.2 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #2,919,787 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

4 of 4 people found the following review helpful:

5.0 out of 5 stars a very good graduate-level book on analysis of algorithms, October 24, 2001

By 

"yreznik" (Seattle, WA United States) - See all my reviews

This review is from: Average Case Analysis of Algorithms on Sequences (Wiley Series in Discrete Mathematics and Optimization) (Hardcover)

If you have ever been curious to know what is the mathematics behind the fancy formulas describing the average-case behavior of algorithms -- this book is for you. An excellent addition to the classic "The Art of Computer Programming" by D.Knuth, "Introduction to Analysis of Algorithms" by R.Sedgewick and P.Flajolet, and "Analysis of Algorithms" by M.Hofri, this book walks reader through a beautiful, and at the same time very diverse (not to say complex) world of mathematic tools and techniques needed to obtain precise answers to questions like "what is the average depth of a digital tree built over $n$ strings?", or "what is the average number of comparisons performed by a Knuth-Morris-Pratt algorithm when it searches for a given pattern of length $m$ in a random text of length $n$?".

Being well organized, the book present these (sometimes very sophisticated) techniques in a simple step-by-step fashion, starting with brief reviews of several known (and necessary for future presentation) results from probability, complex analysis/special functions, and information theory. The presentation of the numerous specific techniques is split in two parts: explaining probabilistic and analytic approaches to the analysis of algorithms correspondingly. Probabilistic techniques (inequalities of moments, limit theorems, large deviations, etc.) are very useful in the analysis of complex random structures, as they often yield simple estimates of their asymptotic behavior, where more accurate techniques fail or become prohibitively laborious. Analytic techniques (generating functions, singularity analysis, saddle point techniques, Mellin transform, analytic poissonization and depoissonization) on the other hand, represent a toolbox for exact modelling of the characteristics of the algorithms, yielding estimates of unparalleled precision.

As indicated by its title, this book is mostly devoted to the analysis of a special class of combinatorial algorithms -- ones that operate with sequences of symbols, or sequences. For example, it includes a detailed analysis of various algorithms for searching and sorting alphanumeric sequences based on digital trees (tries, digital search tries, Patricia-tries, etc.), redundancy expressions for popular Lempel-Ziv data compression schemes, average complexity estimates for text pattern-matching algorithms (such as Knuth-Morris-Pratt scheme), and so on.

Following the famous tradition of "The Art of Computer Programming", the author wraps many (in some case very difficult to derive) results in the form of exercises, so that active readers can have fun solving them. As a special bonus, some of these "exercises" represent currently open research problems.

Overall, this is a very good graduate-level textbook and a valuable (and almost self-contained) source of information for everyone interested in the analysis of algorithms.

2 of 2 people found the following review helpful:

5.0 out of 5 stars a very good graduate-level book on analysis of algorithms, October 24, 2001

By 

"yreznik" (Seattle, WA United States) - See all my reviews

This review is from: Average Case Analysis of Algorithms on Sequences (Wiley Series in Discrete Mathematics and Optimization) (Hardcover)

If you have ever been curious to know what is the mathematics behind the fancy formulas describing the average-case behavior of algorithms -- this book is for you. An excellent addition to the classic "The Art of Computer Programming" by D.Knuth, "Introduction to Analysis of Algorithms" by R.Sedgewick and P.Flajolet, and "Analysis of Algorithms" by M.Hofri, this book walks reader through a beautiful, and at the same time very diverse (not to say complex) world of mathematical tools and techniques needed to obtain precise answers to questions like "what is the average depth of a digital tree built over $n$ strings?", or "what is the average number of comparisons performed by a Knuth-Morris-Pratt algorithm when it searches for a given pattern of length $m$ in a random text of length $n$?".

Being well organized, the book present these (sometimes very sophisticated) techniques in a simple step-by-step fashion, starting with brief reviews of several known (and necessary for future presentation) results from probability, complex analysis/special functions, and information theory. The presentation of the numerous specific techniques is split in two parts: explaining probabilistic and analytic approaches to the analysis of algorithms correspondingly. Probabilistic techniques (inequalities of moments, limit theorems, large deviations, etc.) are very useful in the analysis of complex random structures, as they often yield simple estimates of their asymptotic behavior, where more accurate techniques fail or become prohibitively laborious. Analytic techniques (generating functions, singularity analysis, saddle point techniques, Mellin transform, analytic poissonization and depoissonization) on the other hand, represent a toolbox for exact modelling of the characteristics of the algorithms, yielding estimates of unparalleled precision.

As indicated by its title, this book is mostly devoted to the analysis of a special class of combinatorial algorithms - ones that operate with sequences of symbols, or sequences. For example, it includes a detailed analysis of various algorithms for searching and sorting alphanumeric sequences based on digital trees (tries, digital search tries, Patricia-tries, etc.), redundancy expressions for popular Lempel-Ziv data compression schemes, average complexity estimates for text pattern-matching algorithms (such as Knuth-Morris-Pratt scheme), and so on.

Following the tradition of "The Art of Computer Programming", the author wraps many results in the form of exercises, so that active readers can have fun solving them. These excersises are grouped into several classes, ranging from simple routine calculations to serious research problems (including ones that are currently unsolved).

Overall, this is a very good graduate-level textbook and a valuable (and almost self-contained) source of information for everyone interested in the analysis of algorithms.