The space complexity of approximating the frequency moments

Noga Alon, Yossi Matias, Mario Szegedy

Research output: Chapter in Book/Report/Conference proceedingConference contribution

516 Scopus citations

Abstract

The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = Σn i=1 mki. We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly, it turns out that the numbers F0, F1 and F2 can be approximated in logarithmic space, whereas the approximation of Fk for k ≥ 6 requires nΩ(1) space. Applications to data bases are mentioned as well.

Original languageEnglish (US)
Title of host publicationProceedings of the 28th Annual ACM Symposium on Theory of Computing, STOC 1996
PublisherAssociation for Computing Machinery
Pages20-29
Number of pages10
ISBN (Electronic)0897917855
DOIs
StatePublished - Jul 1 1996
Event28th Annual ACM Symposium on Theory of Computing, STOC 1996 - Philadelphia, United States
Duration: May 22 1996May 24 1996

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
VolumePart F129452
ISSN (Print)0737-8017

Other

Other28th Annual ACM Symposium on Theory of Computing, STOC 1996
CountryUnited States
CityPhiladelphia
Period5/22/965/24/96

All Science Journal Classification (ASJC) codes

  • Software

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