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

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 o...

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Published in:arXiv.org
Main Authors: Chakraborty, Sourav, Vinodchandran, N V, Meel, Kuldeep S
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 24.05.2023
Subjects:
Data transmission
Hash based algorithms
Probability theory
ISSN:2331-8422
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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.
AbstractList 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.
Author Meel, Kuldeep S
Chakraborty, Sourav
Vinodchandran, N V
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Snippet 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...
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Hash based algorithms
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