This book provides a comprehensive introduction to the average case analysis of algorithms on sequences, combining both analytical and probabilistic tools to provide a unified framework for the analysis of algorithms on words. Written in a clear and accessible style, it is suitable for both graduate students and researchers in the field.
The book begins by introducing the basic concepts of words and algorithms on words, covering topics such as string matching algorithms, pattern matching algorithms, compression algorithms, and data structures for words. It then introduces probabilistic models for words, including random words, Markov chains, hidden Markov models, context-free grammars, and Bayesian networks.
The book also introduces analytical models for words, including asymptotic analysis, generating functions, Mellin transforms, the inclusion-exclusion principle, and large deviations. It then introduces the subadditive ergodic theorem and its applications to data compression, pattern matching, computational molecular biology, and security.
The book also covers the inclusion-exclusion principle and its applications, first and second moment methods and their applications, complex asymptotic methods and their applications, analytic Poissonization and depoissonization and their applications, and elements of information theory and their applications.
Finally, the book discusses applications of average case analysis of algorithms on sequences to data compression, pattern matching, computational molecular biology, security, and other areas.
With its comprehensive coverage of the topic, clear and accessible writing style, and wealth of applications, this book is an essential resource for anyone working in the field of average case analysis of algorithms on sequences.
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