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Cardinality Estimation Using Gumbel Distribution

Authors Aleksander Łukasiewicz , Przemysław Uznański

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Author Details

Aleksander Łukasiewicz
  • Faculty of Mathematics and Computer Science, University of Wrocław, Poland
Przemysław Uznański
  • Faculty of Mathematics and Computer Science, University of Wrocław, Poland

Funding

  • Łukasiewicz, Aleksander: Polish National Science Centre grant 2019/33/B/ST6/00298.
  • Uznański, Przemysław: Polish National Science Centre grant 2019/33/B/ST6/00298.

Acknowledgements

We would like to thank Seth Pettie for useful remarks that helped us improve the paper.

Cite AsGet BibTex

Aleksander Łukasiewicz and Przemysław Uznański. Cardinality Estimation Using Gumbel Distribution. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 76:1-76:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ESA.2022.76

Abstract

Cardinality estimation is the task of approximating the number of distinct elements in a large dataset with possibly repeating elements. LogLog and HyperLogLog (c.f. Durand and Flajolet [ESA 2003], Flajolet et al. [Discrete Math Theor. 2007]) are small space sketching schemes for cardinality estimation, which have both strong theoretical guarantees of performance and are highly effective in practice. This makes them a highly popular solution with many implementations in big-data systems (e.g. Algebird, Apache DataSketches, BigQuery, Presto and Redis). However, despite having simple and elegant formulation, both the analysis of LogLog and HyperLogLog are extremely involved - spanning over tens of pages of analytic combinatorics and complex function analysis. We propose a modification to both LogLog and HyperLogLog that replaces discrete geometric distribution with the continuous Gumbel distribution. This leads to a very short, simple and elementary analysis of estimation guarantees, and smoother behavior of the estimator.

Subject Classification

ACM Subject Classification
  • Theory of computation → Sketching and sampling
Keywords
  • Streaming algorithms
  • Cardinality estimation
  • Sketching
  • Gumbel distribution

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