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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. [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.
We consider the sorted top-$k$ problem whose goal is to recover the top-$k$ items with the correct order out of $n$ items using pairwise comparisons. In many applications, multiple rounds of interaction can be costly. We restrict our attention to alg
This paper investigates trajectory prediction for robotics, to improve the interaction of robots with moving targets, such as catching a bouncing ball. Unexpected, highly-non-linear trajectories cannot easily be predicted with regression-based fittin
Trajectory similarity computation is a fundamental component in a variety of real-world applications, such as ridesharing, road planning, and transportation optimization. Recent advances in mobile devices have enabled an unprecedented increase in the
The problem of finding paths in temporal graphs has been recently considered due to its many applications. In this paper we consider a variant of the problem that, given a vertex-colored temporal graph, asks for a path whose vertices have distinct co
The Jaccard index is an important similarity measure for item sets and Boolean data. On large datasets, an exact similarity computation is often infeasible for all item pairs both due to time and space constraints, giving rise to faster approximate m