A fast implementation of near neighbors queries for Fr\'echet distance (GIS Cup)

TL;DR

This paper presents a fast, practical implementation for near-neighbors queries based on the Fréchet distance, utilizing a quadtree and heuristic filters to efficiently handle GPS trajectory data.

Contribution

It introduces a novel recursive algorithm for exact Fréchet distance computation and demonstrates its effectiveness in a practical, competitive setting.

Findings

Implementation won the ACM SIGSPATIAL GIS Cup 2017.

Efficient filtering reduces the number of exact distance computations.

Approach is suitable for large GPS trajectory datasets.

Abstract

This paper describes an implementation of fast near-neighbours queries (also known as range searching) with respect to the Fr\'echet distance. The algorithm is designed to be efficient on practical data such as GPS trajectories. Our approach is to use a quadtree data structure to enumerate all curves in the database that have similar start and endpoints as the query curve. On these curves we run positive and negative filters to narrow the set of potential results. Only for those trajectories where these heuristics fail, we compute the Fr\'echet distance exactly, by running a novel recursive variant of the classic free-space diagram algorithm. Our implementation won the ACM SIGSPATIAL GIS Cup 2017.