We study the problem of finding the k most similar trajectories in a graph to a given query trajectory. Our work was inspired by the work of Grossi et al. [6] that considered trajectories as walks in a graph in which each visited vertex is accompanied by a time-interval. Grossi et al. define a similarity function which is able to capture both temporal and spatial aspects. We modify this similarity function in order to derive a  spatio-temporal distance function for which we can show that a specific type of triangle inequality is satisfied. \% This distance function builds the basis for our index structure which is able to quickly answer queries for the top-k most similar trajectories. Our evaluation on real-world and synthetic data sets shows that our new approaches outperform the baselines with respect to indexing time , query time , and quality of results.
We study the problem of finding the k most similar trajectories to a given query trajectory. Our work is inspired by the work of Grossi et al. [6] that considers trajectories as walks in a graph . Each visited vertex is accompanied by a time-interval. Grossi et al. define a similarity function that captures temporal and spatial aspects. We improve this similarity function to derive a new spatio-temporal distance function for which we can show that a specific type of triangle inequality is satisfied. This distance function is the basis for our index structures, which can be constructed efficiently, need only linear memory, and can quickly answer queries for the top-k most similar trajectories. Our evaluation on real-world and synthetic data sets shows that our algorithms outperform the baselines with respect to indexing time by several orders of magnitude while achieving similar or better query time and quality of results.
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