The space complexity of approximating the frequency moments

Noga Alon, Yossi Matias, Mario Szegedy

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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
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 - 1 Jul 1996
Event28th Annual ACM Symposium on Theory of Computing, STOC 1996 - Philadelphia, United States
Duration: 22 May 199624 May 1996

Publication series

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

Conference

Conference28th Annual ACM Symposium on Theory of Computing, STOC 1996
Country/TerritoryUnited States
CityPhiladelphia
Period22/05/9624/05/96

Funding

FundersFunder number
Fund for Basic Research
USA-Israel BSF
Israel Academy of Sciences and Humanities

    Cite this