Computing multidimensional aggregates in high dimensions is a performance bottleneck for many OLAP applications. Obtaining the exact answer to an aggregation query can be prohibitively expensive in terms of time and or storage space in a data warehouse environment. It is advantageous to have fast, approximate answers to OLAP aggregation queries. In this paper, we present a novel method that provides approximate answers to high-dimensional OLAP aggregation queries in massive sparse data sets in a time-e cient and space-e cient manner. We construct a compact data cube, which is an approximate and space-e cient representation of the underlying multidimensional array, based upon a multiresolution wavelet decomposition. In the on-line phase, each aggregation query can generally be answered using the compact data cube in one I O or a small number of I Os, depending upon the desired accuracy. We present two I O-e cient algorithms to construct the compact data cube for the important case of s...