Devdatt P. Dubhashi, Alessandro Panconesi

Concentration of Measure for the Analysis of Randomized Algorithms

• Gebundenes Buch

Produktbeschreibung

Presents a coherent and unified account of classical and more advanced techniques for analyzing the performance of randomized algorithms. The presentation emphasizes discrete settings and elementary notions of probability, making it accessible to computer scientists and applied discrete mathematicians. The methods are compared by applying them to concrete problems.

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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.

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 214
• Erscheinungstermin: 30. Juli 2014
• Englisch
• Abmessung: 235mm x 157mm x 17mm
• Gewicht: 450g
• ISBN-13: 9780521884273
• ISBN-10: 0521884276
• Artikelnr.: 25686714

Autorenporträt

Devdatt P. Dubhashi is Professor in the Department of Computer Science and Engineering at Chalmers University, Sweden. He earned a Ph.D. in computer science from Cornell University and held positions at the Max-Planck-Institute for Computer Science in Saarbruecken, BRICS, the University of Aarhus and IIT Delhi. Dubhashi has published widely at international conferences and in journals, including many special issues dedicated to best contributions. His research interests span the range from combinatorics to probabilistic analysis of algorithms, and more recently, to computational systems biology and distributed information systems such as the Web.

Inhaltsangabe

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.

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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.

Rezensionen

Review of the hardback: 'It is beautifully written, contains all the major concentration results, and is a must to have on your desk.' Richard Lipton