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

Document Type

Conference Article

Publication Title

Leibniz International Proceedings in Informatics, LIPIcs

Abstract

Given a data stream D = (a1, a2, . . . , am) of m elements where each ai ∈ [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.

DOI

10.4230/LIPIcs.ESA.2022.34

Publication Date

9-1-2022

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