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Formalization of Randomized Approximation Algorithms for Frequency Moments
| Title: | Formalization of Randomized Approximation Algorithms for Frequency Moments |
| Author: | Emin Karayel |
| Submission date: | 2022-04-08 |
| Abstract: | In 1999 Alon et. al. introduced the still active research topic of approximating the frequency moments of a data stream using randomized algorithms with minimal space usage. This includes the problem of estimating the cardinality of the stream elements - the zeroth frequency moment. But, also higher-order frequency moments that provide information about the skew of the data stream. (The k-th frequency moment of a data stream is the sum of the k-th powers of the occurrence counts of each element in the stream.) This entry formalizes three randomized algorithms for the approximation of F0, F2 and Fk for k ≥ 3 based on [1, 2] and verifies their expected accuracy, success probability and space usage. |
| BibTeX: |
@article{Frequency_Moments-AFP,
author = {Emin Karayel},
title = {Formalization of Randomized Approximation Algorithms for Frequency Moments},
journal = {Archive of Formal Proofs},
month = apr,
year = 2022,
note = {\url{https://isa-afp.org/entries/Frequency_Moments.html},
Formal proof development},
ISSN = {2150-914x},
}
|
| License: | BSD License |
| Depends on: | Bertrands_Postulate, Equivalence_Relation_Enumeration, Interpolation_Polynomials_HOL_Algebra, Lp, Median_Method, Prefix_Free_Code_Combinators, Universal_Hash_Families |
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