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Taylor Polynomial Estimator for Estimating Frequency Moments
- Publication Year :
- 2015
-
Abstract
- We present a randomized algorithm for estimating the $p$th moment $F_p$ of the frequency vector of a data stream in the general update (turnstile) model to within a multiplicative factor of $1 \pm \epsilon$, for $p > 2$, with high constant confidence. For $0 < \epsilon \le 1$, the algorithm uses space $O( n^{1-2/p} \epsilon^{-2} + n^{1-2/p} \epsilon^{-4/p} \log (n))$ words. This improves over the current bound of $O(n^{1-2/p} \epsilon^{-2-4/p} \log (n))$ words by Andoni et. al. in \cite{ako:arxiv10}. Our space upper bound matches the lower bound of Li and Woodruff \cite{liwood:random13} for $\epsilon = (\log (n))^{-\Omega(1)}$ and the lower bound of Andoni et. al. \cite{anpw:icalp13} for $\epsilon = \Omega(1)$.<br />Comment: Supercedes arXiv:1104.4552. Extended Abstract of this paper to appear in Proceedings of ICALP 2015
- Subjects :
- Computer Science - Data Structures and Algorithms
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1506.01442
- Document Type :
- Working Paper