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 ChernoffaHoeffding 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 ChernoffaHoeffding 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.Such a result is of obvious importance to the analysis of randomized algorithms: for instance, the running time of such an algorithm ... Often this is because the methods are couched in the technical language of analysis and/or measure theory.
|Title||:||Concentration of Measure for the Analysis of Randomized Algorithms|
|Author||:||Devdatt P. Dubhashi, Alessandro Panconesi|
|Publisher||:||Cambridge University Press - 2009-06-15|