HyperLogLog for probabilists
Data Structures and Algorithms
2026-07-24 v1 Probability
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.
Cite
@article{arxiv.2607.22063,
title = {HyperLogLog for probabilists},
author = {Lucas Gerin},
journal= {arXiv preprint arXiv:2607.22063},
year = {2026}
}