In multi-dimensional database environments, such as those typically associated with contemporary data warehousing, we generally require effective indexing mechanisms for all but the smallest data sets. While numerous such methods have been proposed, the R-tree has emerged as one of the most common and reliable indexing models. Nevertheless, as user queries grow in terms of both size and dimensionality, R-tree performance can deteriorate significantly. Moreover, in the multi-terabyte spaces of today’s enterprise warehouses, the combination of data and indexes ? R-tree or otherwise ? can produce unacceptably large storage requirements. In this chapter, the authors present a framework that addresses both of these concerns. First, they propose a variation of the classic R-tree that specifically targets data warehousing architectures. Their new LBF R-tree not only improves performance on common user-defined range queries, but gracefully degrades to a linear scan of the data on pathologically large queries. Experimental results demonstrate a reduction in disk seeks of more than 50% relative to more conventional R-tree designs. Second, the authors present a fully integrated, block-oriented compression model that reduces the storage footprint of both data and indexes. It does so by exploiting the same Hilbert space filling curve that is used to construct the LBF R-tree itself. Extensive testing demonstrates compression rates of more than 90% for multi-dimensional data, and up to 98% for the associated indexes.
Hilbert space filling curve using scilab
