CIKM '93 Proceedings of the second international conference on Information and knowledge management
Relaxing the uniformity and independence assumptions using the concept of fractal dimension
Journal of Computer and System Sciences - Special issue on principles of database systems
A greedy algorithm for bulk loading R-trees
Proceedings of the 6th ACM international symposium on Advances in geographic information systems
Direct spatial search on pictorial databases using packed R-trees
SIGMOD '85 Proceedings of the 1985 ACM SIGMOD international conference on Management of data
R-trees: a dynamic index structure for spatial searching
SIGMOD '84 Proceedings of the 1984 ACM SIGMOD international conference on Management of data
STR: A Simple and Efficient Algorithm for R-Tree Packing
ICDE '97 Proceedings of the Thirteenth International Conference on Data Engineering
An Evaluation of Generic Bulk Loading Techniques
Proceedings of the 27th International Conference on Very Large Data Bases
VLDB '94 Proceedings of the 20th International Conference on Very Large Data Bases
Hilbert R-tree: An Improved R-tree using Fractals
VLDB '94 Proceedings of the 20th International Conference on Very Large Data Bases
R-Trees: Theory and Applications (Advanced Information and Knowledge Processing)
R-Trees: Theory and Applications (Advanced Information and Knowledge Processing)
The priority R-tree: A practically efficient and worst-case optimal R-tree
ACM Transactions on Algorithms (TALG)
Locality and bounding-box quality of two-dimensional space-filling curves
Computational Geometry: Theory and Applications
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Two-dimensional R-trees are a class of spatial index structures in which objects are arranged to enable fast window queries: report all objects that intersect a given query window. One of the most successful methods of arranging the objects in the index structure is based on sorting the objects according to the positions of their centers along a two-dimensional Hilbert space-filling curve. Alternatively, one may use the coordinates of the objects' bounding boxes to represent each object by a four-dimensional point, and sort these points along a four-dimensional Hilbert-type curve. In experiments by Kamel and Faloutsos and by Arge et al., the first solution consistently outperformed the latter when applied to point data, while the latter solution clearly outperformed the first on certain artificial rectangle data. These authors did not specify which four-dimensional Hilbert-type curve was used; many exist. In this article, we show that the results of the previous articles can be explained by the choice of the four-dimensional Hilbert-type curve that was used and by the way it was rotated in four-dimensional space. By selecting a curve that has certain properties and choosing the right rotation, one can combine the strengths of the two-dimensional and the four-dimensional approach into one, while avoiding their apparent weaknesses. The effectiveness of our approach is demonstrated with experiments on various datasets. For real data taken from VLSI design, our new curve yields R-trees with query times that are better than those of R-trees that were obtained with previously used curves.