Attribute Value Reordering for Efficient Hybrid

The normalization of a data cube is the process of choosing an ordering for the attribute values, and the chosen ordering will affect the physical storage of the cube’s data. For large multidimensional arrays, proper normalization can lead to more efficient storage in hybrid OLAP contexts that store dense and sparse chunks differently. We show that it is NP-hard to compute an optimal normalization even for 1× 3 chunks, although we find an exact algorithm for 1× 2 chunks. When attributes are nearly statistically independent, we show that an optimal normalization is given by dimension-wise attribute frequency sorting, which can be done in time O(dn log(n)) for data cubes of size nd . When attributes are not independent, we propose and evaluate a number of heuristics. The hybrid OLAP storage mechanism, using a naïve normalization, was observed to be 19%–30% more storage efficient than ROLAP. However, when normalization is done carefully, another 9%–13% is gained, and our optimized hybrid OLAP storage mechanism was 29%–44% more storage efficient than ROLAP.