Knowledge and Information Systems

, Volume 55, Issue 1, pp 141–169 | Cite as

The largest empty circle with location constraints in spatial databases

  • Gilberto Gutiérrez
  • Juan R. López
  • José R. Paramá
  • Miguel R. Penabad
Regular Paper


Given a set S of points in the two-dimensional space, which are stored in a spatial database, this paper presents an efficient algorithm to find, in the area delimited by those points, the empty circle with the largest area that contains only a query point q. Our algorithm adapts previous work in the field of computational geometry to be used in spatial databases, which requires to manage large amounts of data. To achieve this objective, the basic idea is to discard a large part of the points of S, in such a way that the problem can be solved providing only the remaining points to a classical computational geometry algorithm that, by processing a smaller collection of points, saves main memory resources and computation time. The correctness of our algorithm is formally proven. In addition, we empirically show its efficiency and scalability by running a set of experiments using both synthetic and real data.


Spatial databases Query processing Geographical information systems Largest empty circle 


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Copyright information

© Springer-Verlag London Ltd. 2017

Authors and Affiliations

  • Gilberto Gutiérrez
    • 2
  • Juan R. López
    • 1
  • José R. Paramá
    • 1
  • Miguel R. Penabad
    • 1
  1. 1.Facultade de Informática, CITICUniversidade da CoruñaA CoruñaSpain
  2. 2.Computer Science and Information Technologies DepartmentUniversidad del Bío-BíoChillánChile

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