Tail Bounds for Occupancy Problems
- Paul Spirakis
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Keywords and Synonyms
Balls and bins
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.
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. 59-80
- 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. Chapman-Hall, Boca Raton
- Weiss, A.: Personal Communication (1993)
- Tail Bounds for Occupancy Problems
- Reference Work Title
- Encyclopedia of Algorithms
- pp 1-99
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- Springer US
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- Editor Affiliations
- 1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University
- Paul Spirakis (1)
- Author Affiliations
- 1. Computer Engineering and Informatics, Research and Academic Computer Technology Institute, Patras University, Patras, Greece
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