Hilbert R-tree: An Improved R-tree using Fractals

We propose a new R-tree structure that outperforms all the older ones. The heart of the idea is to facilitate the deferred splitting approach in R-trees. This is done by proposing an ordering on the R-tree nodes. This ordering has to be `good', in the sense that it should group `similar' data rectangles together, to minimize the area and perimeter of the resulting minimum bounding rectangles (MBRs). Following [Kamel93] we have chosen the so-called `2D-c' method, which sorts rectangles according to the Hilbert value of the center of the rectangles. Given the ordering, every node has a well-defined set of sibling nodes; thus, we can use deferred splitting. By adjusting the split policy, the Hilbert R-tree can achieve as high utilization as desired. To the contrary, the R*-tree has no control over the space utilization, typically achieving up to 70%. We designed the manipulation algorithms in detail, and we did a full implementation of the Hilbert R-tree. Our experiments show that the `2-to-3' split policy provides a compromise between the insertion complexity and the search cost, giving up to 28% savings over the R*-tree [Beckmann90] on real data.