An efficient multidimensional L ∞ $L_{\infty }$ wavelet method and its application to approximate query processing

Approximate query processing (AQP) has been an effective approach for real-time and online query processing for today’s query systems. It provides approximate but fast query results to users. In wavelet based AQP, queries are executed against the wavelet synopsis which is a lossy, compressed representation of the original data returned by a specific wavelet method. Wavelet synopsis optimized for $L_{\infty }$ -norm error can guarantee approximate error of each individual element, thus it can provide error guaranteed query results for many queries. However, most algorithms for building one dimensional $L_{\infty }$ synopsis are of super linear complexity, which makes the extension to their multidimensional case challengeable. In this paper, we propose an efficient multidimensional wavelet method towards constructing $L_{\infty }$ synopsis and we apply it to AQP. The proposed wavelet method can bound the approximate error of each individual element and it has linear time complexity. It can also provide fast AQP. These good properties are all verified theoretically. Extensive experiments on both synthetic and real-life datasets are presented to show its effectiveness and efficiency for data compression and AQP.