Hilbert R-tree: An Improved R-tree Using Fkactals

We propose a new Rtree structure that outperforms all the older ones. The heart of the idea is to facilitate the deferred splitting ap preach 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 to gether, to minimize the area and perimeter of the resulting minimum bounding rectangles (MBRs). Following [KF93] 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 *This resexch was partially fuuded by the hmtitutc for Systerm, FLsemch (ISR), by the National Science Foundation under Grants IF&9205273 and IFU-8958546 (PYI), with matching fuuds from EMPRESS Software Inc. und Think& h4achinen