Abstract
We discuss a spatio-temporal data structure to index objects moving on a graph. It is designed to efficiently answer rectangle R plus time instance and time interval queries about the past positions of moving objects. Such data structures are useful, for example, when searching which vehicles moving on a road network in specific areas at specific times. Unlike other data structures that use R-trees to index bounding boxes of moving object trajectories, our data structure indexes oriented line segments representing positions of moving objects at different times. For n moving object instances (unique entries of moving objects) on a graph with E edges, we show that \(O(log_2 E + |L| log_2^2(n/E) + k)\) time is required to answer a rectangle R plus time interval query, for |L| the number of edges intersected by R and k the number of line segments containing moving object instances in range. Space O(n 2/E + E) is required in the worst case to store n moving object instances in E ordered polyline trees. Space Ω(n + E) is required to store the history of all n moving object instances.
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Le, T.T.T., Nickerson, B.G. (2010). Ordered Polyline Trees for Efficient Search of Objects Moving on a Graph. In: Taniar, D., Gervasi, O., Murgante, B., Pardede, E., Apduhan, B.O. (eds) Computational Science and Its Applications – ICCSA 2010. ICCSA 2010. Lecture Notes in Computer Science, vol 6016. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12156-2_31
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DOI: https://doi.org/10.1007/978-3-642-12156-2_31
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