Hierarchical Compact Cube for Range-Max Queries

A range-max query finds the maximum value over all selected cells of an on-line analytical processing (OLAP) data cube where the selection is specified by ranges of contiguous values for each dimension. One of the approaches to process such queries is to precompute a prefix cube (PC), which is a cube of the same dimensionality and size as the original data cube, but with some pre-computed results stored in each cell. In this paper, we propose a new cube representation called Hierarchical Compact Cube, which is an hierarchical structure that stores not only the maximum value of all the children sub-cubes, but also stores one of the locations of the maximum values among the children sub-cubes. The storage requirement is much less than the prefix cube methods. Furthermore, both of our analysis and experiment results show that the average query time using our method is bounded by a constant independent on the number of data in the data cube, N. For a fixed dimension, the average update cost of our new structure in the worst case is also relatively low. It is only O(log N).