Computing unrestricted synopses under maximum error bound

Abstract

Constructing Haar wavelet synopses with guaranteed maximum error on data approximations has many real world applications. In this paper, we take a novel approach towards constructing unrestricted Haar wavelet synopses under maximum error metrics (L ∞). We first provide two linear time (logN)-approximation algorithms which have space complexities of O(logN) 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 methods are very compact and scalable, and sympathetic for online data processing. We then demonstrate that this technique can be extended to other findings such as Haar+ tree. Extensive experiments indicate that these techniques are highly practical. The proposed algorithms achieve a very attractive tradeoff between efficiency and effectiveness, surpassing contemporary (logN)-approximation algorithms in compressing qualities. © 2011 Springer Science+Business Media, LLC.