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2005
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Optimal approximations of the frequency moments of data streams

12 years 9 months ago
Optimal approximations of the frequency moments of data streams
We give a 1-pass ~O(m1-2/k )-space algorithm for computing the k-th frequency moment of a data stream for any real k > 2. Together with the lower bounds of [1, 2, 4], this resolves the main problem left open by Alon et al in 1996 [1]. Our algorithm also works for streams with deletions and thus gives an ~O(m1-2/p ) space algorithm for the Lp difference problem for any p > 2. This essentially matches the known (m1-2/p-o(1) ) lower bound of [13, 2]. Finally the update time of our algorithm is ~O(1). Categories and Subject Descriptors F.2 [ Theory of Computation]: ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY General Terms Algorithms Keywords Streaming algorithms, frequency moments
Piotr Indyk, David P. Woodruff
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2005
Where STOC
Authors Piotr Indyk, David P. Woodruff
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