Abstract
We provide in this article a branch-and-bound algorithm that solves the problem of finding the k closest pairs of points (p,q), p ∈ P,q ∈ Q, considering two sets of points in the euclidean plane P,Q stored in external memory assuming that only one of the sets has a spatial index. This problem arises naturally in many scenarios, for instance when the set without an index is the answer to a spatial query. The main idea of our algorithm is to partition the space occupied by the set without an index into several cells or subspaces and to make use of the properties of a set of metrics defined on two Minimum Bounding Rectangles (MBRs). We evaluated our algorithm for different values of k by means of a series of experiments that considered both synthetical and real world datasets. We compared the performance of our algorithm with that of techniques that either assume that both datasets have a spatial index or that none has an index. The results show that our algorithm needs only between a 0.3 and a 35 % of the disk accesses required by such techniques. Our algorithm also shows a good scalability, both in terms of k and of the size of the data set.
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Notes
1K = 1,000 points.
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Acknowledgements
We are grateful to Miguel Pincheira for providing a software that simulates the algorithm in [18], to Antonio Corral for some kind suggestions and to two anonymous referees for many observations that helped us improve this article.
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This work was partially supported by the research project DIUBB 073218 A/R, and was partially done in the context of a postdoctoral stay by the first author at the University of A Coruña (Spain), supported by project MECESUP UBB0704.
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Gutiérrez, G., Sáez, P. The k closest pairs in spatial databases. Geoinformatica 17, 543–565 (2013). https://doi.org/10.1007/s10707-012-0169-4
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DOI: https://doi.org/10.1007/s10707-012-0169-4