Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Frequency Moments

  • David WoodruffEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_167


Lp distances; Lp norms


Consider a stream (i.e., an ordered list) = a1 , a2 … , an of elements ai ∈ [m]def = {1, 2, … , m}. For i ∈ [m], its frequency fi is the number of times it occurs in . The kth frequency moment Fk of , for real k > 0, is defined to be \( {F}_k({\cal S})={\displaystyle {\sum}_{i\in \left[m\right]}{f}_i^k} \)

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Recommended Reading

  1. 1.
    Alon N, Matias Y, Szegedy M. The space complexity of approximating the frequency moments. J Comput Syst Sci. 1999;58(1):137–47.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Bar-Yossef Z, Jayram T, Kumar R, Sivakumar D. An information statistics approach to data stream and communication complexity. In: Proceedings of the 43rd Annual Symposium on Foundations of Computer Science; 2002. p. 209–18.Google Scholar
  3. 3.
    Indyk P, Woodruff D. Optimal approximations of the frequency moments of data streams. In: Proceedings of the 37th Annual ACM Symposium on Theory of Computing; 2005. p. 202–8.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.IBM Almaden Research CenterSan JoseUSA

Section editors and affiliations

  • Divesh Srivastava
    • 1
  1. 1.AT&T Labs - ResearchAT&TBedminsterUSA