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...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	arXiv.org
Hauptverfasser:	Chakraborty, Sourav, Vinodchandran, N V, Meel, Kuldeep S
Format:	Paper
Sprache:	Englisch
Veröffentlicht:	Ithaca Cornell University Library, arXiv.org 24.05.2023
Schlagworte:	Data transmission Hash based algorithms Probability theory
ISSN:	2331-8422
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	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.
Bibliographie:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.2301.10191