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Concentration of Measure for the Analysis of Randomized Algorithms

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ISBN-10: 1107606608

ISBN-13: 9781107606609

Edition: 2012

Authors: Devdatt P. Dubhashi, Alessandro Panconesi

List price: $56.95
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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 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.
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Book details

List price: $56.95
Copyright year: 2012
Publisher: Cambridge University Press
Publication date: 3/12/2012
Binding: Paperback
Pages: 214
Size: 6.25" wide x 9.50" long x 0.75" tall
Weight: 0.748
Language: English

Devdatt 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 to, more recently, 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.

Chernoff-Hoeffding bounds
Applying the CH-bounds
CH-bounds with dependencies
Interlude: probabilistic recurrences
Martingales and the MOBD
The MOBD in action
Averaged bounded difference
The method of bounded variances
Interlude: the infamous upper tail
Isoperimetric inequalities and concentration
Talagrand inequality
Transportation cost and concentration
Transportation cost and Talagrand's inequality
Log-Sobolev inequalities
Summary of the most useful bounds