On Practical Nearest Sub-Trajectory Queries under the Fréchet Distance

Abstract

We study the problem of sub-trajectory nearest-neighbor queries on polygonal curves under the continuous Fréchet distance. Given a trajectory P with n vertices and a query trajectory Q, we seek to report a vertex-aligned sub-trajectory P' of P that is closest to Q, i.e. P' must start and end on contiguous vertices of P. Since in real data P typically contains a very large number of vertices, we focus on answering queries exactly, without restrictions on P or Q, using only pre-computed structures of O(n) size. We use three baseline algorithms from straightforward extensions of known work, however they have impractical performance on realistic inputs. Therefore, we propose a new Hierarchical Simplification Tree data structure and an adaptive clustering based query algorithm that efficiently explores relevant parts of P. Experiments on real and synthetic data show that our heuristic effectively prunes the search space and greatly reduces computations compared to baseline approaches.