Finding the Largest Empty Rectangle Containing Only a Query Point in Large Multidimensional Databases

  • Gilberto Gutiérrez
  • José R. Paramá
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7338)


Given a two-dimensional space, let S be a set of points stored in an R-tree, let R be the minimum rectangle containing the elements of S, and let q be a query point such that q ∉ S and R ∩ q ≠ ∅. In this paper, we present an algorithm for finding the empty rectangle with the largest area, sides parallel to the axes of the space, and containing only the query point q. The idea behind algorithm is to use the points that define the minimum bounding rectangles (MBRs) of some internal nodes of the R-tree to avoid reading as many nodes of the R-tree as possible, given that a naive algorithm must access all of them. We present several experiments considering synthetic and real data. The results show that our algorithm uses around 0.71–38% of the time and around 3–4% of the main storage needed by previous computational geometry algorithms. Furthermore, to the best of our knowledge, this is the first work that solves this problem considering that the points are stored in an R-tree.


Geographical Information System Main Memory Query Point Real Point Naive Approach 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Gilberto Gutiérrez
    • 1
  • José R. Paramá
    • 2
  1. 1.Departamento de Ciencias de la Computación y Tecnologías de la InformaciónUniversidad del Bío-BíoChillánChile
  2. 2.Department of Computer ScienceUniversity of A CoruñaEspaña

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