“Balls into Bins” — A Simple and Tight Analysis

  • Martin Raab
  • Angelika Steger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1518)


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.


Binomial Distribution Moment Method Load Balance Problem Tail Bound Chernoff Bound 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [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
  2. [Bol85]
    B. Bollobás. Random graphs. Academic Press, New York-San Francisco-London-San Diego, 1985.zbMATHGoogle Scholar
  3. [CS97]
    A. Czumaj and V. Stemann. Randomized allocation processes. In 38th Annual Symposium on Foundations of Computer Science, pages 194–203, 1997.Google Scholar
  4. [Gon81]
    G.H. Gonnet. Expected length of the longest probe sequence in hash code searching. J. ACM, 28(2):289–304, 1981.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [JK77]
    N. Johnson and S. Kotz. Urn Models and Their Applications. John Wiley and Sons, 1977.Google Scholar
  6. [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

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Martin Raab
    • 1
  • Angelika Steger
    • 1
  1. 1.Institut für InformatikTechnische Universität MünchenMünchen

Personalised recommendations