On the Value of Multiple Read/Write Streams for Approximating Frequency Moments

We consider the read/write streams model, an extension of the standard data stream model in which an algorithm can create and manipulate multiple read/write streams in addition to its input data stream. We show that any randomized read/write stream algorithm with a fixed number of streams and a sublogarithmic number of passes that produces a constant factor approximation of the k-th frequency moment Fk of an input sequence of length of at most N from {1, . . . , N} requires space Ω(N1−4/k−δ ) for any δ > 0. For comparison, it is known that with a single read-only data stream there is a randomized constantfactor approximation for Fk using ˜O(N1−2/k ) space and that there is a deterministic algorithm computing Fk exactly using 3 read/write streams, O(log N) passes, and O(log N) space. Therefore, although the ability to manipulate multiple read/write streams can add substantial power to the data stream model, with a sub-logarithmic number of passes this does not significa...

• Type: Conference
• Year: 2008
• Where: FOCS
• Authors: Paul Beame, Dang-Trinh Huynh-Ngoc
• Keywords: Data Stream, FOCS 2008, Multiple Read/write Streams, Read/write Streams, Theoretical Computer Science