Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
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Information Fusion
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Sensor networks are unattended deeply distributed systems whose schema can be conceptualized using the relational model. Aggregation queries on the data sampled at each sensor node are the main means to extract the abstract characteristics of the surrounding environment. However, the non-uniform distribution of the sensor nodes in the environment leads to inaccurate results generated by the aggregation queries. In this paper, we introduce "spatial aggregations" that take into consideration the distribution of the values generated by the sensor nodes. We propose the use of spatial interpolation methods derived from the fields of spatial statistics and computational geometry to answer spatial aggregations. In particular, we study Spatial Moving Average (SMA), Voronoi Diagram and Triangulated Irregular Network (TIN). Investigating these methods for answering spatial average queries, we show that the average value on the data samples weighted by the area of the Voronoi cell of the corresponding sensor node, provides the best precision. Consequently, we introduce an incremental algorithm to compute and maintain the Voronoi cell at each sensor node. To demonstrate the performance of in-network implementation of our algorithm, we have developed prototypes of two different approaches to distributed spatial aggregate processing.