One-pass wavelet synopses for maximum-error metrics

Abstract

We study the problem of computing wavelet-based synopses for massive data sets in static and streaming environments. A compact representation of a data set is obtained after a thresholding process is applied on the coefficients of its wavelet decomposition. Existing polynomial-time thresholding schemes that minimize maximum error metrics are disadvantaged by impracticable time and space complexities and are not applicable in a data stream context. This is a cardinal issue, as the problem at hand in its most practically interesting form involves the time-efficient approximation of huge amounts of data, potentially in a streaming environment. In this paper we fill this gap by developing efficient and practicable wavelet thresholding algorithms for maximum-error metrics, for both a static and a streaming case. Our algorithms achieve near-optimal accuracy and superior runtime performance, as our experiments show, under frugal space requirements in both contexts.