Data Cube Approximation and Histograms via Wavelets

Abstract

There has recently been an explosion of interest in the analysis of data in data warehouses in the field of On-Line Analytical Processing (OLAP). Data warehouses can be extremely large, yet obtaining quick answers to queries is important. In many situations, obtaining the exact answer to an OLAP query is prohibitively expensive in terms of time and/or storage space. It can be advantageous to have fast, approximate answers to queries. In this paper, we present an I/O-efficient technique based upon a multiresolution wavelet decomposition that yields an approximate and space-efficient representation of the data cube, which is one of the core OLAP operators. We build our compact data cube on the logarithms of the partial sums of the raw data values of a multidimensional array. We get excellent approximations for on-line range-sum queries with limited space usage and computational cost. Multiple data cubes can be handled simultaneously. Each query can generally be answered, depending upon the accuracy supported, in one I/O or a small number of I/Os. Experiments show that our method performs significantly better than other approximation techniques such as histograms and random sampling.