Tight Lower Bound for Linear Sketches of Moments
Author(s)Andoni, Alexandr; Nguyen, Huy L.; Polyanskiy, Yury; Wu, Yihong
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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.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Automata, Languages, and Programming
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.
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