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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| Vydáno v: | arXiv.org |
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| Hlavní autoři: | , , |
| Médium: | Paper |
| Jazyk: | angličtina |
| Vydáno: |
Ithaca
Cornell University Library, arXiv.org
24.05.2023
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| Témata: | |
| ISSN: | 2331-8422 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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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| Bibliografie: | SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50 |
| ISSN: | 2331-8422 |
| DOI: | 10.48550/arxiv.2301.10191 |