Concentration of Measure for the Analysis of Randomized Algorithms

This book presents a coherent and unified account of classical and more advanced techniques for analyzing the performance of randomized algorithms.

Devdatt P. Dubhashi (Author), Alessandro Panconesi (Author)

9780521884273, Cambridge University Press

Hardback, published 15 June 2009

214 pages, 12 b/w illus. 168 exercises
22.9 x 15.2 x 1.6 cm, 0.45 kg

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

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.

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.

Subject Areas: Algorithms & data structures [UMB], Stochastics [PBWL], Probability & statistics [PBT], Geometry [PBM], Algebra [PBF], Discrete mathematics [PBD]