Approximating the Fréchet Distance When Only One Curve Is c-Packed
Joachim Gudmundsson, Tiancheng Mai, Sampson Wong · arXiv (Cornell University) · 2024
One approach to studying the Fréchet distance is to consider curves that satisfy realistic assumptions. By now, the most popular realistic assumption for curves is c-packedness. Existing algorithms for computing the Fréchet distance between c-packed curves require both curves to be c-packed. In this paper, we only require one of the two curves to be c-packed. Our result is a nearly-linear time algorithm that (1+ε)-approximates the Fréchet distance between a c-packed curve and a general curve in ℝ^d, for constant values of ε, d and c.