Zero-One Frequency Laws

Data streams emerged as a critical model for multiple applications that handle vast amounts of data. One of the most influential and celebrated papers in streaming is the “AMS” paper on computing frequency moments by Alon, Matias and Szegedy. The main question left open (and explicitly asked) by AMS in 1996 is to give the precise characterization for which functions G on frequency vectors mi (1 ≤ i ≤ n) can i∈[n] G(mi) be approximated efficiently, where “efficiently” means by a single pass over data stream and poly-logarithmic memory. No such characterization was known despite a tremendous amount of research on frequency-based functions in streaming literature. In this paper we finally resolve the AMS main question and give a precise characterization (in fact, a zero-one law) for all monotonically increasing functions on frequencies that are zero at the origin. That is, we consider all monotonic functions G : R → R such that G(0) = 0 and G can be computed in poly-log...

• Type: Conference
• Year: 2010
• Where: STOC
• Authors: Vladimir Braverman and Rafail Ostrovsky
• Keywords: Data Stream, Main Question, Precise Characterization, STOC 2010