HyperLogLog for probabilists — Draconitic Research

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

BibTeX RIS

BibTeX

@misc{gerin2026hyperloglog,
  title = {{HyperLogLog for probabilists}},
  author = {Lucas Gerin},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.22063},
  eprint = {2607.22063},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05702505v2},
  note = {CC BY-NC-SA 4.0},
}

RIS

TY  - UNPB
TI  - HyperLogLog for probabilists
AU  - Lucas Gerin
PY  - 2026
DA  - 2026/10/08
PB  - HAL
DO  - 10.48550/arxiv.2607.22063
UR  - https://hal.science/hal-05702505v2
AB  - 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.
ER  -