Approximating Large Frequency Moments with Bits
V Braverman, J Katzman, C Seidell… - arXiv preprint arXiv …, 2014 - arxiv.org
V Braverman, J Katzman, C Seidell, G Vorsanger
arXiv preprint arXiv:1401.1763, 2014•arxiv.orgIn this paper we consider the problem of approximating frequency moments in the streaming
model. Given a stream $ D=\{p_1, p_2,\dots, p_m\} $ of numbers from $\{1,\dots, n\} $, a
frequency of $ i $ is defined as $ f_i=|\{j: p_j= i\}| $. The $ k $-th\emph {frequency moment} of
$ D $ is defined as $ F_k=\sum_ {i= 1}^ n f_i^ k $. In this paper we give an upper bound on
the space required to find a $ k $-th frequency moment of $ O (n^{1-2/k}) $ bits that matches,
up to a constant factor, the lower bound of Woodruff and Zhang (STOC 12) for constant …
model. Given a stream $ D=\{p_1, p_2,\dots, p_m\} $ of numbers from $\{1,\dots, n\} $, a
frequency of $ i $ is defined as $ f_i=|\{j: p_j= i\}| $. The $ k $-th\emph {frequency moment} of
$ D $ is defined as $ F_k=\sum_ {i= 1}^ n f_i^ k $. In this paper we give an upper bound on
the space required to find a $ k $-th frequency moment of $ O (n^{1-2/k}) $ bits that matches,
up to a constant factor, the lower bound of Woodruff and Zhang (STOC 12) for constant …
In this paper we consider the problem of approximating frequency moments in the streaming model. Given a stream of numbers from , a frequency of is defined as . The -th \emph{frequency moment} of is defined as . In this paper we give an upper bound on the space required to find a -th frequency moment of bits that matches, up to a constant factor, the lower bound of Woodruff and Zhang (STOC 12) for constant and constant . Our algorithm makes a single pass over the stream and works for any constant .
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