Fast moment estimation in data streams in optimal space

Daniel M. Kane, Jelani Nelson, Ely Porat, David P. Woodruff

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

65 Scopus citations

Abstract

We give a space-optimal streaming algorithm with update time O(log 2(1/ε)loglog(1/ε)) for approximating the pth frequency moment, 0 < p < 2, of a length-n vector updated in a data stream up to a factor of 1 ± ε. This provides a nearly exponential improvement over the previous space optimal algorithm of [Kane-Nelson-Woodruff, SODA 2010], which had update time Ω(1/ε2). When combined with the work of [Harvey-Nelson-Onak, FOCS 2008], we also obtain the first algorithm for entropy estimation in turnstile streams which simultaneously achieves near-optimal space and fast update time.

Original languageEnglish
Title of host publicationSTOC'11 - Proceedings of the 43rd ACM Symposium on Theory of Computing
PublisherAssociation for Computing Machinery
Pages745-754
Number of pages10
ISBN (Print)9781450306911
DOIs
StatePublished - 2011
Event43rd ACM Symposium on Theory of Computing, STOC 2011 - San Jose, United States
Duration: 6 Jun 20118 Jun 2011

Publication series

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

Conference

Conference43rd ACM Symposium on Theory of Computing, STOC 2011
Country/TerritoryUnited States
CitySan Jose
Period6/06/118/06/11

Keywords

  • data stream algorithms
  • frequency moments

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