An Introduction to the Analysis of Algorithms

[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 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 Combinatoricsand in Donald Knuth's Art of Computer Programmingbooks-and provide the background they need to keep abreast of new research.

Robert Sedgewick is the William O. Baker Professor of Computer Science at Princeton University, where was founding chair of the computer science department and has been a member of the faculty since 1985. He is a Director of Adobe Systems and has served on the research staffs at Xerox PARC, IDA, and INRIA. He is the coauthor of the landmark introductory book, Algorithms, Fourth Edition. Professor Sedgewick earned his Ph.D from Stanford University under Donald E. Knuth.

 

The late Philippe Flajolet was a Senior Research Director at INRIA, Rocquencourt, where he created and led the ALGO research group. He is celebrated for having opened new lines of research in the analysis of algorithms; having systematized and developed powerful new methods in the field of analytic combinatorics; having solved numerous difficult, open problems; and having lectured on the analysis of algorithms all over the world. Dr. Flajolet was a member of the French Academy of Sciences.

Foreword

Preface

Note on the Second Edition

 

Chapter 1: Analysis of Algorithms

Chapter 2: Recurrence Relations

Chapter 3: Generating Functions

Chapter 4: Asymptotic Approximations

Chapter 5: Analytic Combinatorics

Chapter 6: Trees

Chapter 7: Permutations

Chapter 8: Strings and Tries

Chapter 9: Words and Mappings

 

List of Theorems

Index