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.
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Notes
- 1.
The later case can not be guaranteed by the approach of [6] due to the numeric nature of their approach.
- 2.
We use Euclidean distance in all examples and illustrations, but any \(L_p\) norm can be applied.
- 3.
recall that if \(e_{max}^{\mathcal {D}}\) corresponds to case 3, then there exists no \(R^*\)-entry such that case 4 holds.
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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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Emrich, T., Schmid, K.A., Züfle, A., Renz, M., Cheng, R. (2015). Uncertain Voronoi Cell Computation Based on Space Decomposition. In: Claramunt, C., et al. Advances in Spatial and Temporal Databases. SSTD 2015. Lecture Notes in Computer Science(), vol 9239. Springer, Cham. https://doi.org/10.1007/978-3-319-22363-6_6
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