Concentration of Measure for the Analysis of Randomized Algorithms

by Devdatt P. Dubhashi, Alessandro Panconesi

Overview

Randomized algorithms have become a central part of the algorithms curriculum based on their increasingly widespread use in modern applications. This book presents a coherent and unified treatment of probabilistic techniques for obtaining high- probability estimates on the performance of randomized algorithms. It covers the basic tool kit from the Chernoff-Hoeffding (CH) bounds to more sophisticated techniques like Martingales and isoperimetric inequalities, as well as some recent developments like Talagrand's inequality, transportation cost inequalities, and log-Sobolev inequalities. Along the way, variations on the basic theme are examined, such as CH bounds in dependent settings. The authors emphasize comparative study of the different methods, highlighting respective strengths and weaknesses in concrete example applications. The exposition is tailored to discrete settings sufficient for the analysis of algorithms, avoiding unnecessary measure-theoretic details, thus making the book accessible to computer scientists as well as probabilists and discrete mathematicians.

Product Details

ISBN-13:	9780521884273
Publisher:	Cambridge University Press
Publication date:	06/15/2009
Edition description:	New Edition
Pages:	214
Product dimensions:	6.10(w) x 9.10(h) x 0.80(d)

About the Author

Devdatt P. Dubhashi is Professor in the Department of Computer Science and Engineering at Chalmers University, Sweden. He earned a Ph.D. in computer science from Cornell University and held positions at the Max-Planck-Institute for Computer Science in Saarbruecken, BRICS, the University of Aarhus and IIT Delhi. Dubhashi has published widely at international conferences and in journals, including many special issues dedicated to best contributions. His research interests span the range from combinatorics to probabilistic analysis of algorithms, and more recently, to computational systems biology and distributed information systems such as the Web.

Alessandro Panconesi is Professor of Computer Science at Sapienza University of Rome. He earned a Ph.D. in computer science from Cornell University and is the recipient of the 1992 ACM Danny Lewin Award. Panconesi has published more than 50 papers in international journals and selective conference proceedings and he is the associate editor of the Journal of Discrete Algorithms and the director of BiCi, the Bertinoro International Center of Informatics. His research spans areas of algorithmic research as diverse as randomized algorithms, distributed computing, complexity theory, experimental algorithmics, wireless networking and Web information retrieval.

Table of Contents

1. Chernoff–Hoeffding bounds; 2. Applying the CH-bounds; 3. CH-bounds with dependencies; 4. Interlude: probabilistic recurrences; 5. Martingales and the MOBD; 6. The MOBD in action; 7. Averaged bounded difference; 8. The method of bounded variances; 9. Interlude: the infamous upper tail; 10. Isoperimetric inequalities and concentration; 11. Talagrand inequality; 12. Transportation cost and concentration; 13. Transportation cost and Talagrand's inequality; 14. Log–Sobolev inequalities; Appendix A. Summary of the most useful bounds.

Editorial Reviews

Pre-Publication Review: "Concentration bounds are at the core of probabilistic analysis of algorithms. This excellent text provides a comprehensive treatment of this important subject, ranging from the very basic to the more advance tools, including some recent developments in this area. The presentation is clear and includes numerous examples, demonstrating applications of the bounds in analysis of algorithms. This book is a valuable resource for both researches and students in the field."
Eli Upfal, Professor of Computer Science, Brown University, author of "Probability and Computing"

"It is beautifully written, contains all the major concentration results, and is a must to have on your desk."
Rich Lipton

"The book does a superb job of describing a collection of powerful methodologies in a unified manner; what is even more striking is that basic combinatorial and probabilistic language is used in bringing out the power of such approaches. To summarize, the book has done a great job of synthesizing diverse and important material in a very accessible manner. Any student, researcher, or practitioner of computer science, electrical engineering, mathematics, operations research, and related fields, could benefit from this wonderful book. The book would also make for fruitful classes at the undergraduate- and graduate- levels. I highly recommend it."
Aravind Srinivasan, SIGACT News

"The strength of this book is that it is appropriate for both the beginner as well as the experienced researcher in the field of randomized algorithms. I highly recommend this book both as an advanced as well as an introductory textbook, which can also serve the needs of an experienced researcher in algorithmics."
Yannis C. Stamatiou, Mathematical Reviews

"This timely book brings together in a comprehensive and accessible form a sophisticated toolkit of powerful techniques for the analysis of randomized algorithms, illustrating their use with a wide array of insightful examples. This book is an invaluable resource for people venturing into this exciting field of contemporary computer science research."
Prabhakar Ragahavan, Yahoo Research

"Concentration inequalities are an essential tool for the analysis of algorithms in any probabilistic setting. There have been many recent developments on this subject, and this excellent text brings them together in a highly accessible form."
Alan Frieze, Carnegie Mellon University

From the Publisher