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9781107606609

Concentration of Measure for the Analysis of Randomized Algorithms

by ;
  • ISBN13:

    9781107606609

  • ISBN10:

    1107606608

  • Format: Paperback
  • Copyright: 2012-03-31
  • Publisher: Cambridge Univ Pr

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Summary

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.

Table of Contents

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
Table of Contents provided by Publisher. All Rights Reserved.

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