Tight Lower Bound for Linear Sketches of Moments
Name
Polyanskiy_Tight lower.pdf
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329.34 KB
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Author(s)
Andoni, Alexandr
Nguyen, Huy L.
Polyanskiy, Yury
Wu, Yihong
Date Issued
2013
Journal
Automata, Languages, and Programming
Citation
Andoni, Alexandr, Huy L. Nguyen, Yury Polyanskiy, and Yihong Wu. “Tight Lower Bound for Linear Sketches of Moments.” Lecture Notes in Computer Science (2013): 25–32.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://doi.org/10.1007/978-3-642-39206-1_3
