Distinct Elements in Streams: An Algorithm for the (Text) Book
Given a data stream š = āØ a_1, a_2, ā¦, a_m ā© of m elements where each a_i ā [n], the Distinct Elements problem is to estimate the number of distinct elements in š. 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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