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 an n vertex trajectory P and an m vertex query trajectory Q, we seek to report a vertex-aligned sub-trajectory P \prime of P that is closest to Q, i.e. P \prime 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, without restrictions on P or Q, using only precomputed structures of \scrO (n) size.We use three baseline algorithms from straightforward extensions of known work, however they have impractical performance on realistic inputs. erefore, we propose a new Hierarchical Simpli cation Tree data structure and an adaptive clustering based query algorithm that e ciently explores relevant parts of P . e core of our query methods is a novel greedy-backtracking algorithm that solves the Fréchet decision problem using \scrO (n + m) space and \scrO (nm) time in the worst case.Experiments on real and synthetic data show that our heuristic e ectively prunes the search space and greatly reduces computations compared to baseline approaches.