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 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 1 − 2/plogn) words of space [AKO11,BO10], whereas the lower bound is of Ω(n 1 − 2/p) [BJKS04].
In this paper, we show a tight lower bound of Ω(n 1 − 2/plogn) 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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Andoni, A., Nguyễn, H.L., Polyanskiy, Y., Wu, Y. (2013). Tight Lower Bound for Linear Sketches of Moments. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds) Automata, Languages, and Programming. ICALP 2013. Lecture Notes in Computer Science, vol 7965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39206-1_3
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DOI: https://doi.org/10.1007/978-3-642-39206-1_3
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