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arXiv · 2301.10191

Distinct Elements in Streams: An Algorithm for the (Text) Book

Sourav Chakraborty·N. V. Vinodchandran·Kuldeep S. Meel
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Abstract

Given a data stream $\mathcal{A} = \langle a_1, a_2, \ldots, a_m \rangle$ of $m$ elements where each $a_i \in [n]$, the Distinct Elements problem is to estimate the number of distinct elements in $\mathcal{A}$.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.

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Sourav Chakraborty, N. V. Vinodchandran, Kuldeep S. Meel. 2023-01-24. Distinct Elements in Streams: An Algorithm for the (Text) Book. https://doi.org/10.4230/lipics.esa.2022.34

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