Concentration of Measure for the Analysis of Randomized Algorithms

Erscheinungsjahr 2014
ISBN: 978-0-521-88427-3
Verlag: Cambridge University Press

Buch, Englisch, 216 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 505 g

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.

Autoren/Hrsg.

Dubhashi, Devdatt P.

Dubhashi, Devdatt

Panconesi, Alessandro

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker

Inhaltsverzeichnis

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.

Über Autor(innen)

Panconesi, Alessandro
Alessandro Panconesi is Professor of Computer Science at Sapienza University of Rome. He earned a Ph.D. in computer science from Cornell University and is the recipient of the 1992 ACM Danny Lewin Award. Panconesi has published more than 50 papers in international journals and selective conference proceedings, and he is the Associate Editor of the Journal of Discrete Algorithms and the Director of the Bertinoro International Center of Informatics. His research spans areas of algorithmic research as diverse as computational biology, distributed computing, complexity theory, experimental algorithmics, wireless networking, and IR.

Dubhashi, Devdatt
Devdatt 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 to, more recently, computational systems biology and distributed information systems such as the Web.