Concentration of Measure for the Analysis of Randomized by Devdatt P. Dubhashi,Alessandro Panconesi

By Devdatt P. Dubhashi,Alessandro Panconesi

Randomized algorithms became a critical a part of the algorithms curriculum, in response to their more and more frequent use in sleek purposes. This booklet provides a coherent and unified therapy of probabilistic options for acquiring excessive chance estimates at the functionality of randomized algorithms. It covers the elemental toolkit from the Chernoff–Hoeffding bounds to extra refined concepts like martingales and isoperimetric inequalities, in addition to a few fresh advancements like Talagrand's inequality, transportation expense inequalities and log-Sobolev inequalities. alongside the best way, adaptations at the simple subject are tested, equivalent to Chernoff–Hoeffding bounds in established settings. The authors emphasise comparative learn of the various tools, highlighting respective strengths and weaknesses in concrete instance purposes. The exposition is customized to discrete settings enough for the research of algorithms, keeping off pointless measure-theoretic information, therefore making the ebook available to laptop scientists in addition to probabilists and discrete mathematicians.

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