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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.  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 isarXiv:2009.06778v2 fatcat:hhx5h4spqjhnxgok576n4twn3a