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90562 |
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|a Andoni, Alexandr
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|a Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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|a Polyanskiy, Yury
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|a Nguyen, Huy L.
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|a Polyanskiy, Yury
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|a Wu, Yihong
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|a Tight Lower Bound for Linear Sketches of Moments
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|c 2014-10-06T18:41:47Z.
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|z Get fulltext
|u http://hdl.handle.net/1721.1/90562
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|a 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.
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|a National Science Foundation (U.S.). Center for Science of Information (Grant Agreement CCF-0939370)
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|a en_US
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|a Article
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|t Automata, Languages, and Programming
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