Approximating the Fr\'echet Distance for Realistic Curves in Near Linear Time

TL;DR

This paper introduces a practical algorithm for approximating the Fréchet distance between curves with near linear time complexity for a new class of curves called c-packed curves, which are relevant for real-world applications.

Contribution

The paper presents a simple, practical (1+ε)-approximation algorithm for the Fréchet distance and introduces c-packed curves, a new family of curves that enables near linear time analysis.

Findings

Near linear time algorithm for c-packed curves

Introduction of c-packed curves as a realistic input model

Algorithm achieves (1+ε)-approximation accuracy

Abstract

We present simple and practical $(1+\eps)$-approximation algorithm for the Frechet distance between curves. To analyze this algorithm we introduce a new realistic family of curves, $c$-packed curves, that is closed under simplification. We believe the notion of $c$-packed curves to be of independent interest. We show that our algorithm has near linear running time for $c$-packed curves, and show similar results for other input models.