Translation Invariant Fréchet Distance Queries
Abstract
The Fréchet distance is a popular similarity measure between curves. For some applications, it is desirable to match the curves under translation before computing the Fréchet distance between them. This variant is called the Translation Invariant Fréchet distance, and algorithms to compute it are well studied. The query version, finding an optimal placement in the plane for a query segment where the Fréchet distance becomes minimized, is much less well understood. We study Translation Invariant Fréchet distance queries in a restricted setting of horizontal query segments. More specifically, we preprocess a trajectory in $\mathcal O(n^2 \log^2 n) $ time and $\mathcal O(n^{3/2})$ space, such that for any subtrajectory and any horizontal query segment we can compute their Translation Invariant Fréchet distance in $\mathcal O(\text{polylog } n)$ time. We hope this will be a step towards answering Translation Invariant Fréchet queries between arbitrary trajectories.
 Publication:

arXiv eprints
 Pub Date:
 February 2021
 arXiv:
 arXiv:2102.05844
 Bibcode:
 2021arXiv210205844G
 Keywords:

 Computer Science  Computational Geometry