Definition
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, specifically the Hilbert curve, to impose a linear ordering on the data rectangles.
There are two types of Hilbert R-tree, one for static database and one for dynamic databases. In both cases, space filling curves and specifically the Hilbert curve 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...
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References
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Recommended Reading
Guttman A (1984) R-trees: a dynamic index structure for spatial searching. In: Proceedings of ACM SIGMOD, Boston, June 1984, pp 47–57
Kamel I, Faloutsos C (1992) Parallel R-trees. In: Proceedings of ACM SIGMOD conference, San Diego, June 1992, pp 195–204
Kamel I, Faloutsos C (1994) Hilbert R-tree: an improved R-tree using fractals. In: Proceedings of VLDB conference, Santiago, Sept 1994, pp 500–509
Koudas N, Faloutsos C, Kamel I (1996) Declustering spatial databases on a multi-computer architecture. In: International conference on extending database technology (EDBT), Avignon, 25–29 Mar 1996, pp 592–614
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Sellis T, Roussopoulos N, Faloutsos C (1987) The R+-tree: a dynamic index for multi-dimensional objects. In: Proceedings 13th international conference on VLDB, Brighton, Sept 1987, pp 507–518
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Kamel, I. (2017). Indexing, Hilbert R-Tree, Spatial Indexing, Multimedia Indexing. In: Shekhar, S., Xiong, H., Zhou, X. (eds) Encyclopedia of GIS. Springer, Cham. https://doi.org/10.1007/978-3-319-17885-1_603
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