Randomized algorithms and their applications

Randomized algorithms have become a central part of the algorithms curriculum, based on their increasingly widespread use in modern applications.

Overview of probabilistic techniques

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.

Variations and comparative study

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.

Accessibility and audience

The exposition is tailored to discrete settings sufficient for the analysis of algorithms, avoiding unnecessary measure-theoretic details, as a result making the book accessible to computer scientists as well as probabilists and discrete mathematicians.