Hilbert R-tree

Hilbert R-tree, an R-tree variant, is an index for multidimensional objects like lines, regions, 3-D objects, or high-dimensional feature-based parametric objects. It can be thought of as an extension to B+-tree for multidimensional objects.

The performance of R-trees depends on the quality of the algorithm that clusters the data rectangles on a node. Hilbert R-trees use space-filling curves, and specifically the Hilbert curve, to impose a linear ordering on the data rectangles.

There are two types of Hilbert R-trees, one for static databases, and one for dynamic databases. In both cases Hilbert space-filling curves are used to achieve better ordering of multidimensional objects in the node. 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). Packed Hilbert R-trees are suitable for static databases in which updates are very rare or in which there are no updates at all.