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