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

@inproceedings{DBLP:conf/vldb/KamelF94,
  author    = {Ibrahim Kamel and
               Christos Faloutsos},
  editor    = {Jorge B. Bocca and
               Matthias Jarke and
               Carlo Zaniolo},
  title     = {Hilbert R-tree: An Improved R-tree using Fractals},
  booktitle = {VLDB'94, Proceedings of 20th International Conference on Very
               Large Data Bases, September 12-15, 1994, Santiago de Chile, Chile},
  publisher = {Morgan Kaufmann},
  year      = {1994},
  isbn      = {1-55860-153-8},
  pages     = {500-509},
  ee        = {db/conf/vldb/vldb94-500.html},
  crossref  = {DBLP:conf/vldb/94},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

Abstract

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.

Copyright © 1994 by the VLDB Endowment. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by the permission of the Very Large Data Base Endowment. To copy otherwise, or to republish, requires a fee and/or special permission from the Endowment.

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