Abstract
The R-tree is a well-known bounding-volume hierarchy that is suitable for storing geometric data on secondary memory. Unfortunately, no good analysis of its query time exists. We describe a new algorithm to construct an R-tree for a set of planar objects that has provably good query complexity for point location queries and range queries with ranges of small width. For certain important special cases, our bounds are optimal. We also show how to update the structure dynamically, and we generalize our results to higher-dimensional spaces.
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References
Becker, P. Franciosa, S. Gschwind, T. Ohler, G. Thiemt, and P. Widmayer. Enclosing many boxes by an optimal pair of boxes. In Proc. 9th Annual Symposium on Theoretical Aspects of Computer Science (STACS), LNCS 577, pages 475–486, 1992.
N. Beckmann, H.-P. Kriegel, R. Schneider, and B. Seeger. The R*-tree: an efficient and robust access method for points and rectangles. In Proc. ACM-SIGMOD International Conference on Management of Data, pages 322–331, 1990.
C. Faloutos and I. Kamel. Packed R-trees using fractals. Report CS-TR-3009, University of Maryland, College Park, 1992.
C. Faloutos, T. Sellis, and N. Roussopoulos. Analysis of object oriented spatial access methods. In Proc. ACM-SIGMOD International Conference on Management of Data, pages 426–439, 1987.
D.M. Gavrila. R-tree index optimization. In Proc. 6th Int. Symp. on Spatial Data Handling, pages 771–791, 1994.
D. Greene. An implementation and performance analysis of spatial data access methods. In Proc. 5th International Conference on Data Engineering, pages 606–615, 1989.
A. Guttmann. R-trees: a dynamic indexing structure for spatial searching. In Proc. ACM-SIGMOD International Conference on Management of Data, pages 47–57, 1984.
J. Nievergelt and P. Widmayer. Spatial data structures: concepts and design choices. In M. van Kreveld, J. Nievergelt, T. Roos, and P. Widmayer (eds.), Algorithmic Foundations of Geographic Information Systems, LNCS 1340, pages 153–198, 1997.
N. Roussopoulos and D. Leifer. Direct spatial search on pictorial databases with packed R-trees. In Proc. ACM-SIGMOD International Conference on Management of Data, 1985.
H.-W. Six and P. Widmayer. Spatial access structures for geometric databases. In B. Monien and T. Ottmann (eds.), Data Structures and Efficient Algorithms, LNCS 594, pages 214–232, 1992.
Y. Zhou and S. Suri. Analysis of a bounding box heuristic for object intersection. In Proc. 10th Annual Symposium on Discrete Algorithms (SODA), 1999. To appear in Journal of the ACM.
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de Berg, M., Gudmundsson, J., Hammar, M., Overmars, M. (2000). On R-Trees with Low Stabbing Number. In: Paterson, M.S. (eds) Algorithms - ESA 2000. ESA 2000. Lecture Notes in Computer Science, vol 1879. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45253-2_16
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DOI: https://doi.org/10.1007/3-540-45253-2_16
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