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  3. Concentration of Measure for the Analysis of Randomized Algorithms
  • Cited by 346
Publisher:
Cambridge University Press
Online publication date:
October 2009
Print publication year:
2009
Online ISBN:
9780511581274
DOI:
https://doi.org/10.1017/CBO9780511581274
Subjects:
Algorithmics, Complexity, Computer Algebra, Computational Geometry, Computer Science
Information

Book description

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 toolkit from the Chernoff–Hoeffding 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 Chernoff–Hoeffding bounds in dependent settings. The authors emphasise 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.

Reviews

Review of the hardback:‘It is beautifully written, contains all the major concentration results, and is a must to have on your desk.'

Richard Lipton

Review of the hardback:‘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 advanced 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 researchers and students in the field.'

Eli Upfal - Brown University

Review of the hardback:‘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

Review of the hardback:‘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 Source: SIGACT News

Review of the hardback:‘… 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 … The exposition style […] combines informal discussion with formal definitions and proofs, giving first the intuition and motivation for the probabalistic technique at hand. … 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 Source: Mathematical Reviews

Reviews of the hardback:‘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

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