Tight Lower Bound for Linear Sketches of Moments
The problem of estimating frequency moments of a data stream has attracted a lot of attention since the onset of streaming algorithms [AMS99]. While the space complexity for approximately computing the p [superscript th] moment, for p ∈ (0,2] has been settled [KNW10], for p > 2 the exact complexi...
Main Authors: | , , , |
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Format: | Article |
Language: | English |
Published: |
2014-10-06T18:41:47Z.
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Subjects: | |
Online Access: | Get fulltext |
Summary: | The problem of estimating frequency moments of a data stream has attracted a lot of attention since the onset of streaming algorithms [AMS99]. While the space complexity for approximately computing the p [superscript th] moment, for p ∈ (0,2] has been settled [KNW10], for p > 2 the exact complexity remains open. For p > 2 the current best algorithm uses O(n [superscript 1 − 2/p] logn) words of space [AKO11,BO10], whereas the lower bound is of Ω(n [superscript 1 − 2/p]) [BJKS04]. In this paper, we show a tight lower bound of Ω(n [superscript 1 − 2/p] logn) words for the class of algorithms based on linear sketches, which store only a sketch Ax of input vector x and some (possibly randomized) matrix A. We note that all known algorithms for this problem are linear sketches. National Science Foundation (U.S.). Center for Science of Information (Grant Agreement CCF-0939370) |
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