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An asymptotically optimal algorithm for generating bin cardinalities

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  • Devroye, Luc
  • Los, Dimitrios

Abstract

In the balls-into-bins setting, n balls are thrown uniformly at random into n bins. The naïve way to generate the final load vector takes Θ(n) time. However, it is well-known that this load vector has with high probability bin cardinalities of size Θ(lognloglogn). Here, we present an algorithm in the RAM model that generates the bin cardinalities of the final load vector in the optimal Θ(lognloglogn) time in expectation and with high probability.

Suggested Citation

  • Devroye, Luc & Los, Dimitrios, 2025. "An asymptotically optimal algorithm for generating bin cardinalities," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 228(C), pages 147-155.
    • Handle: RePEc:eee:matcom:v:228:y:2025:i:c:p:147-155
    DOI: 10.1016/j.matcom.2024.08.034
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    References listed on IDEAS

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    1. Davis, Charles S., 1993. "The computer generation of multinomial random variates," Computational Statistics & Data Analysis, Elsevier, vol. 16(2), pages 205-217, August.
    2. A. C. Atkinson, 1979. "The Computer Generation of Poisson Random Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 28(1), pages 29-35, March.
    3. A. C. Atkinson, 1979. "Recent Developments in the Computer Generation of Poisson Random Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 28(3), pages 260-263, November.
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