TY - GEN

T1 - Fast moment estimation in data streams in optimal space

AU - Kane, Daniel M.

AU - Nelson, Jelani

AU - Porat, Ely

AU - Woodruff, David P.

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

KW - data stream algorithms

KW - frequency moments

UR - http://www.scopus.com/inward/record.url?scp=79959741836&partnerID=8YFLogxK

U2 - 10.1145/1993636.1993735

DO - 10.1145/1993636.1993735

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AN - SCOPUS:79959741836

SN - 9781450306911

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 745

EP - 754

BT - STOC'11 - Proceedings of the 43rd ACM Symposium on Theory of Computing

PB - Association for Computing Machinery

T2 - 43rd ACM Symposium on Theory of Computing, STOC 2011

Y2 - 6 June 2011 through 8 June 2011

ER -