|
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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