“Balls into Bins” — A Simple and Tight Analysis
Suppose we sequentially throw m balls into n bins. It is a natural question to ask for the maximum number of balls in any bin. In this paper we shall derive sharp upper and lower bounds which are reached with high probability. We prove bounds for all values of m(n) ≧ n/polylog(n) by using the simple and well-known method of the first and second moment.
KeywordsBinomial Distribution Moment Method Load Balance Problem Tail Bound Chernoff Bound
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- [ABKU92]Y. Azar, A.Z. Broder, A.R. Karlin, and E. Upfal. On-line load balancing (extended abstract). In 33rd Annual Symposium on Foundations of Computer Science, pages 218–225, Pittsburgh, Pennsylvania, 24–27 October 1992. IEEE.Google Scholar
- [CS97]A. Czumaj and V. Stemann. Randomized allocation processes. In 38th Annual Symposium on Foundations of Computer Science, pages 194–203, 1997.Google Scholar
- [JK77]N. Johnson and S. Kotz. Urn Models and Their Applications. John Wiley and Sons, 1977.Google Scholar
- [Mit96]M.D. Mitzenmacher. The Power of Two Choices in Randomized Load Balancing. PhD thesis, Computer Science Department, University of California at Berkeley, 1996.Google Scholar