Periodicity and Cyclic Shifts via Linear Sketches

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Periodicity and Cyclic Shifts via Linear Sketches
We consider the problem of identifying periodic trends in data streams. We say a signal a ∈ Rn is p-periodic if ai = ai+p for all i ∈ [n − p]. Recently, Erg¨un et al. [4] presented a one-pass, O(polylog n)space algorithm for identifying the smallest period of a signal. Their algorithm required a to be presented in the time-series model, i.e., ai is the ith element in the stream. We present a more general linear sketch algorithm that has the advantages of being applicable to a) the turnstile stream model, where coordinates can be incremented/decremented in an arbitrary fashion and b) the parallel or distributed setting where the signal is distributed over multiple locations/machines. We also present sketches for (1+ ) approximating the 2 distance between a and the nearest p-periodic signal for a given p. Our algorithm uses O( −2 polylog n) space, comparing favorably to an earlier time-series result that used O( −5.5√ p polylog n) space for estimating the Hamming distance to...
Michael S. Crouch, Andrew McGregor
Added 12 Dec 2011
Updated 12 Dec 2011
Type Journal
Year 2011
Authors Michael S. Crouch, Andrew McGregor
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