SHIFT-SPLIT: I/O efficient maintenance of wavelet-transformed multidimensional data

The Discrete Wavelet Transform is a proven tool for a wide range of database applications. However, despite broad acceptance, some of its properties have not been fully explored and thus not exploited, particularly for two common forms of multidimensional decomposition. We introduce two novel operations for wavelet transformed data, termed SHIFT and SPLIT, based on the properties of wavelet trees, which work directly in the wavelet domain. We demonstrate their significance and usefulness by analytically proving six important results in four common data maintenance scenarios, i.e., transformation of massive datasets, appending data, approximation of data streams and partial data reconstruction, leading to significant I/O cost reduction in all cases. Furthermore, we show how these operations can be further improved in combination with the optimal coefficient-to-disk-block allocation strategy. Our exhaustive set of empirical experiments with real-world datasets verifies our claims.