Tail Bounds for Occupancy Problems
 Paul Spirakis
 … show all 1 hide
Keywords and Synonyms
Balls and bins
Problem Definition
Consider a random allocation of m balls to n bins where each ball is placed in a bin chosen uniformly and independently. The properties of the resulting distribution of balls among bins have been the subject of intensive study in the probability and statistics literature [3,4]. In computer science, this process arises naturally in randomized algorithms and probabilistic analysis. Of particular interest is the occupancy problem where the random variable under consideration is the number of empty bins.
In this entry a series of bounds are presented (reminiscent of the Chernoff bound for binomial distributions) on the tail of the distribution of the number of empty bins; the tail bounds are successively tighter, but each new bound has a more complex closed form. Such strong bounds do not seem to have appeared in the earlier literature.
Key Results
The following notation in pres ...
 Kamath, A., Motwani, R., Spirakis, P., Palem, K. (1995) Tail bounds for occupancy and the satisfiability threshold conjecture. J. Random Struct. Algorithms 7: pp. 5980
 Janson, S.: Large Deviation Inequalities for Sums of Indicator Variables. Technical Report No. 34, Department of Mathematics, Uppsala University (1994)
 Johnson, N.L., Kotz, S. (1977) Urn Models and Their Applications. Wiley, New York
 Kolchin, V.F., Sevastyanov, B.A., Chistyakov, V.P. (1978) Random Allocations. Wiley, New York
 Motwani, R., Raghavan, P. (1995) Randomized Algorithms. Cambridge University Press, New York
 Shwartz, A., Weiss, A. (1994) Large Deviations for Performance Analysis. ChapmanHall, Boca Raton
 Weiss, A.: Personal Communication (1993)
 Title
 Tail Bounds for Occupancy Problems
 Reference Work Title
 Encyclopedia of Algorithms
 Pages
 pp 199
 Copyright
 2008
 DOI
 10.1007/9780387301624_419
 Print ISBN
 9780387307701
 Online ISBN
 9780387301624
 Publisher
 Springer US
 Copyright Holder
 SpringerVerlag
 Additional Links
 Topics
 Industry Sectors
 eBook Packages
 Editors
 Editor Affiliations

 1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University
 Authors

 Paul Spirakis ^{(1)}
 Author Affiliations

 1. Computer Engineering and Informatics, Research and Academic Computer Technology Institute, Patras University, Patras, Greece
Continue reading...
To view the rest of this content please follow the download PDF link above.