Massive datasets of curves, such as time series and trajectories, are continuously generated by mobile and sensing devices. A relevant operation on curves is similarity search: given a dataset S of curves, construct a data structure that, for any query curve q, finds the curves in S similar to q. Similarity search is a computational demanding task, in particular when a robust distance function is used, such as the continuous Fr\'echet distance. In this paper, we propose FRESH, a novel approximate solution to find similar curves under the continuous Fr\'echet distance. FRESH leverages on a locality sensitive hashing scheme for detecting candidate near neighbors of the query curve, and  a subsequent pruning step based on a pipeline of curve simplifications. By relaxing the requirement of exact and deterministic solutions, FRESH reaches high performance and outperforms the state-of-the-art approaches. The experiments indeed show that, with a recall larger than 80\% and precision 100\%, we have at least a factor 10 improvement in performance over a baseline given by the best solutions developed for the ACM SIGSPATIAL 2017 challenge on the Fr\'echet distance . Furthermore, the improvement peaks up to two orders of magnitude, and even more, by relaxing the precision.
Massive datasets of curves, such as time series and trajectories, are continuously generated by mobile and sensing devices. A relevant operation on curves is similarity search: given a dataset S of curves, construct a data structure that, for any query curve q, finds the curves in S similar to q. Similarity search is a computational demanding task, in particular when a robust distance function is used, such as the continuous Fr\'echet distance. In this paper, we propose FRESH, a novel approximate solution to find similar curves under the continuous Fr\'echet distance. FRESH leverages on a locality sensitive hashing scheme for detecting candidate near neighbors of the query curve, and on a subsequent pruning step based on a cascade of curve simplifications. By relaxing the requirement of exact and deterministic solutions, FRESH reaches high performance : the experiments indeed show that, with a recall larger than 80\% and precision 100\%, we have at least a factor 10 improvement in performance over the state-of-the-art exact approach . Furthermore, the improvement peaks up to two orders of magnitude, and even more, by relaxing the precision.
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a baseline given by the best solutions developed for the ACM SIGSPATIAL 2017 challenge on the Fr\'echet distance
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