Year: 2026
Type: preprint
Abstract: HyperLogLog is a now classic probabilistic algorithm that provides an approximation of the number of distinct elements in a massive dataset, using only one pass over the data. In the original article, Flajolet, Fusy, Gandouet, Meunier (2007) provided a sharp analysis of the expectation and variance of the output, using explicit formulas analyzed using poissonization and Mellin transform. In this short article, we revisit the analysis of HyperLogLog with a more probabilistic viewpoint. This allows us to establish exponential deviation inequalities for the HyperLogLog estimator. The methods are elementary, but the estimates are non-asymptotic and totally explicit.
Source: arXiv (Cornell University)
Author: Gerin, Lucas
Institution: Modélisation aléatoire de Paris Nanterre
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7171381160