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

• Type: Conference
• Year: 2005
• Where: STOC
• Authors: Piotr Indyk, David P. Woodruff
• Keywords: Algorithms, ALGORITHMS AND PROBLEM, Keywords Streaming Algorithms, Lp Difference Problem, STOC 2005