Unrestricted wavelet synopses under maximum error bound

Abstract

Constructing Haar wavelet synopses under a given approximation error has many real world applications. In this paper, we take a novel approach towards constructing unrestricted Haar wavelet synopses under an error bound on uniform norm (L∞). We provide two approximation algorithms which both have linear time complexity and a (log N)-approximation ratio. The space complexities of these two algorithms are O (log N) and O (N) respectively. These two algorithms have the advantage of being both simple in structure and naturally adaptable for stream data processing. Unlike traditional approaches for synopses construction that rely heavily on examining wavelet coefficients and their summations, the proposed construction methods solely depend on examining the original data and are extendable to other findings. Extensive experiments indicate that these techniques are highly practical and surpass related ones in both efficiency and effectiveness.