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The largest empty rectangle containing only a query object in Spatial Databases

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Abstract

Let S be a set of n points in a fixed axis-parallel rectangle \(R\subseteq \Re^{2}\), i.e. in the two-dimensional space (2D). Assuming that those points are stored in an R-tree, this paper presents several algorithms for finding the empty rectangle in R with the largest area, sides parallel to the axes of the space, and containing only a query point q. This point can not be part of S, that is, it is not stored in the R-tree. All algorithms follow the basic idea of discarding part of the points of S, in such a way that the problem can be solved only considering the remaining points. As a consequence, the algorithms only have to access a very small portion of the nodes (disk blocks) of the R-tree, saving main memory resources and computation time. We provide formal proofs of the correctness of our algorithms and, in order to evaluate the performance of the algorithms, we run an extensive set of experiments using synthetic and real data. The results have demonstrated the efficiency and scalability of our algorithms for different dataset configurations.

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Notes

  1. computeER only computes LQMER, instead of computing all QMERs.

  2. http://libspatialindex.github.com/

  3. 1 K = 1,000 points

  4. http://rtreeportal.org

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Acknowledgements

This work was supported, for the first author, by the project MECESUP UBB0704 (Chile). For the second and third authors by Ministerio de Educación y Ciencia [TIN2009-14560-C03-02] and [TIN2010-21246-C02-01], and Xunta de Galicia [grant 2010/17]. Finally, for the last author, his work has been supported by the Ministerio de Educación y Ciencia [TIN2008-003063], and the Junta de Andalucía research project [TIC-06114]. We would like to thank Yannis Manolopoulos and Juan Ramón López Rodríguez for their valuable comments and suggestions to improve the quality of the paper.

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Authors and Affiliations

  1. Computer Science and Information Technologies Department, Universidad del Bío-Bío, Chillán, Chile

    Gilberto Gutiérrez

  2. Computer Science Department, University of A Coruña, A Coruña, Spain

    José R. Paramá & Nieves Brisaboa

  3. Department of Languages and Computation, University of Almeria, Almeria, Spain

    Antonio Corral

Authors
  1. Gilberto Gutiérrez
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  2. José R. Paramá
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  3. Nieves Brisaboa
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  4. Antonio Corral
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Corresponding author

Correspondence to Gilberto Gutiérrez.

Additional information

A preliminary partial version of this work appeared in [16].

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Gutiérrez, G., Paramá, J.R., Brisaboa, N. et al. The largest empty rectangle containing only a query object in Spatial Databases. Geoinformatica 18, 193–228 (2014). https://doi.org/10.1007/s10707-013-0178-y

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