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.

近似查询处理（AQP）已成为当今查询系统实时和在线查询处理的有效方法。它向用户提供近似但快速的查询结果。在基于小波的AQP中，针对小波提要执行查询，该提要是由特定小波方法返回的原始数据的有损压缩表示。针对\（L _ {\ infty} \）- norm误差进行了优化的小波提要可以保证每个元素的近似误差，因此可以为许多查询提供保证误差的查询结果。但是，大多数用于构建一维\（L _ {\ infty} \）的算法提要具有超线性的复杂性，这使得对其多维情况的扩展提出了挑战。在本文中，我们提出了一种有效的多维小波方法来构造\（L _ {\ infty} \）提要，并将其应用于AQP。提出的小波方法可以限制每个单独元素的近似误差，并且具有线性时间复杂度。它还可以提供快速的AQP。这些良好的性能在理论上都得到了验证。提出了对合成数据集和真实数据集的大量实验，以证明其对于数据压缩和AQP的有效性和效率。