LIPIcs.ESA.2022.34.pdf
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Distinct Elements in Streams: An Algorithm for the (Text) Book
Authors
Sourav Chakraborty 
,
N. V. Vinodchandran¹ ,
Kuldeep S. Meel
-
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Volume:
30th Annual European Symposium on Algorithms (ESA 2022)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: European Symposium on Algorithms (ESA) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2022-09-01
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Sourav Chakraborty, N. V. Vinodchandran¹, and Kuldeep S. Meel. Distinct Elements in Streams: An Algorithm for the (Text) Book. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 34:1-34:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ESA.2022.34
https://doi.org/10.4230/LIPIcs.ESA.2022.34
Abstract
Given a data stream 𝒟 = ⟨ a₁, a₂, …, a_m ⟩ of m elements where each a_i ∈ [n], the Distinct Elements problem is to estimate the number of distinct elements in 𝒟. Distinct Elements has been a subject of theoretical and empirical investigations over the past four decades resulting in space optimal algorithms for it. All the current state-of-the-art algorithms are, however, beyond the reach of an undergraduate textbook owing to their reliance on the usage of notions such as pairwise independence and universal hash functions. We present a simple, intuitive, sampling-based space-efficient algorithm whose description and the proof are accessible to undergraduates with the knowledge of basic probability theory.
Subject Classification
ACM Subject Classification
- Theory of computation → Sketching and sampling
Keywords
- F₀ Estimation
- Streaming
- Sampling
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References
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