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SODA
2004
ACM

Optimal space lower bounds for all frequency moments

8 years 4 months ago
Optimal space lower bounds for all frequency moments
We prove that any one-pass streaming algorithm which ( , )-approximates the kth frequency moment Fk, for any real k = 1 and any = 1 m , must use 1 2 bits of space, where m is the size of the universe. This is optimal in terms of , resolves the open questions of BarYossef et al in [3, 4], and extends the 1 2 lower bound for F0 in [11] to much smaller by applying novel techniques. Along the way we lower bound the one-way communication complexity of approximating the Hamming distance and the number of bipartite graphs with minimum/maximum degree constraints.
David P. Woodruff
Added 31 Oct 2010
Updated 31 Oct 2010
Type Conference
Year 2004
Where SODA
Authors David P. Woodruff
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