Distinct Elements In Streams An Algorithm For The (text) Book
Chakraborty Sourav, Vinodchandran N. V., Meel Kuldeep S.. Apppeared in Proceedings of 2023
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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