An asymptotically optimal algorithm for generating bin cardinalities

Luc Devroye and Dimitrios Los

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 228, issue C, 147-155

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.

Keywords: Random variate generation; Simulation; Expected time analysis; Balls-into-bins; Random allocations; Hashing (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:228:y:2025:i:c:p:147-155

DOI: 10.1016/j.matcom.2024.08.034

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