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Average Case Analysis of Algorithms on Sequences

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
Product Details

Table of Contents

Foreword. Preface. Acknowledgments. PROBLEMS ON WORDS. Data Structures and Algorithms on Words. Probabilistic and Analytical Models. PROBABILISTIC AND COMBINATORIAL TECHNIQUES. Inclusion-Exclusion Principle. The First and Second Moment Methods. Subadditive Ergodic Theorem and Large Deviations. Elements of Information Theory. ANALYTIC TECHNIQUES. Generating Functions. Complex Asymptotic Methods. Mellin Transform and Its Applications. Analytic Poissonization and Depoissonization. Bibliography. Index.

About the Author

WOJCIECH SZPANKOWSKI, PhD, is Professor of Computer Science at Purdue University and has held visiting research positions at the Technical University of Gdansk, McGill University, INRIA, the Technical University of Vienna, University of Witwatersrand, Hewlett-Packard Laboratories, and Stanford University. He is the author of over 100 scientific publications in the areas of analysis of algorithms, information theory, performance evaluation of computer networks, stability of distributed systems, and queueing theory.


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

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