Generalizing the Layering Method of Indyk and Woodruff: Recursive Sketches for Frequency-Based Vectors on Streams

In their ground-breaking paper, Indyk and Woodruff (STOC 05) showed how to compute the k-th frequency moment F k (for k > 2) in space O(poly − log(n,m) · n\(^{1-{2} \over{k}})\), giving the first optimal result up to poly-logarithmic factors in n and m (here m is the length of the stream and n is the size of the domain.) The method of Indyk and Woodruff reduces the problem of F k to the problem of computing heavy hitters in the streaming manner. Their reduction only requires polylogarithmic overhead in term of the space complexity and is based on the fundamental idea of “layering.” Since 2005 the method of Indyk and Woodruff has been used in numerous applications and has become a standard tool for streaming computations.

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