Fast Fréchet Distance Between Curves with Long Edges
Joachim Gudmundsson, Majid Mirzanezhad, Ali Mohades, Carola Wenk · International Journal of Computational Geometry & Applications · 2018
Computing Fréchet distance between two curves takes roughly quadratic time. The only strongly subquadratic time algorithm has been proposed in [7] for c-packed curves. In this paper, we show that for curves with long edges the Fréchet distance computations become easier. Let P and Q be two polygonal curves in Rd with n and m vertices, respectively. We prove three main results for the case when all edges of both curves are long compared to the Fréchet distance between them: (1) a linear-time algorithm for deciding the Fréchet distance between two curves, (2) an algorithm that computes the Fréchet distance in O((n + m) log(n + m)) time, and (3) a linear-time [EQUATION]-approximation algorithm for approximating the Fréchet distance between two curves.