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Uncertain Voronoi Cell Computation Based on Space Decomposition

  • Tobias Emrich
  • Klaus Arthur Schmid
  • Andreas Züfle
  • Matthias Renz
  • Reynold Cheng
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9239)

Abstract

The problem of computing Voronoi cells for spatial objects whose locations are not certain has been recently studied. In this work, we propose a new approach to compute Voronoi cells for the case of objects having rectangular uncertainty regions. Since exact computation of Voronoi cells is hard, we propose an approximate solution. The main idea of this solution is to apply hierarchical access methods for both data and object space. Our space index is used to efficiently find spatial regions which must (not) be inside a Voronoi cell. Our object index is used to efficiently identify Delauny relations, i.e., data objects which affect the shape of a Voronoi cell. We develop three algorithms to explore index structures and show that the approach that descends both index structures in parallel yields fast query processing times. Our experiments show that we are able to approximate uncertain Voronoi cells much more effectively than the state-of-the-art, and at the same time, improve run-time performance.

Notes

Acknowledgements

Part of the research leading to these results has received funding from the Deutsche Forschungsgemeinschaft (DFG) under grant number RE 266/5-1 and from the DAAD supported by BMBF under grant number 57055388. Reynold Cheng was supported by the Research Grants Council of Hong Kong (RGC Project (HKU 711110)).

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Tobias Emrich
    • 1
  • Klaus Arthur Schmid
    • 1
  • Andreas Züfle
    • 1
  • Matthias Renz
    • 1
  • Reynold Cheng
    • 2
  1. 1.Institute for InformaticsLudwig-Maximilians-Universität MünchenMünchenGermany
  2. 2.Department of Computer ScienceUniversity of Hong KongHong KongChina

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