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.

• Type: Conference
• Year: 2004
• Where: SODA
• Authors: David P. Woodruff
• Keywords: Algorithms, Frequency Moment Fk, Lower Bound, One-pass Streaming Algorithm, SODA 2004