Integrating DCT and DWT for approximating cube streams

Abstract

For time-relevant multi-dimensional data sets (MDS), users usually pose a huge amount of data due to the large dimensionality, and approximating query processing has emerged as a viable solution. Specifically, the cube streams handle MDSs in a continuous manner. Traditional cube approximation focuses on generating single snapshots rather than continuous ones. To address this issue, the application of generating snapshots for cube streams, called SCS, is investigated in this paper. Such an application collects data events for cube streams on-line and generates snapshots with limited resources in order to keep the approximated information in synopsis memory for further analysis. As compared to OLAP applications, the SCS ones are subject to much more resource constraints for both processing time and memory and cannot be dealt with by existing methods due to the limited resources. In this paper, the DAWA algorithm, standing for a hybrid algorithm of Dct for Data and discrete WAvelet transform, is proposed to approximate the cube streams. The DAWA algorithm combines the advantage of high compression rate from DWT and that of low memory cost from DCT. Consequently, DAWA costs much smaller working buffer and outperforms both DWT-based and DCT-based methods in execution efficiency. Also, it is shown that DAWA provides answers of good quality for SCS applications with a small working buffer and short execution time. The optimality of algorithm DAWA is theoretically proved and also empirically demonstrated by our experiments. Copyright 2005 ACM.