On Multidimensional Wavelet Synopses for Maximum Error Bounds

Abstract

Having been extensively used to summarize massive data sets, wavelet synopses can be classified into two types: space-bounded and error-bounded synopses. Although various research efforts have been made for the space-bounded synopses construction, the constructions of error-bounded synopses are yet to be thoroughly studied. The state-of-the-art approaches on error-bounded synopses mainly focus on building one-dimensional wavelet synopses, while efficient algorithms on constructing multidimensional error-bounded wavelet synopses still need to be investigated. In this paper, we propose a first linear approximate algorithm to construct multidimensional error-bounded L _∞-synopses. Our algorithm constructs a synopsis that has O(logn) approximation ratio to the size of the optimal solution. Experiments on two-dimensional array data have been conducted to support the theoretical aspects of our algorithm. Our method can build two-dimensional wavelet synopses in less than 1 second for a large data set up to 1024×1024 data array under given error bounds. The advantages of our algorithm is further demonstrated through other comparisons in terms of synopses construction time and synopses sizes.