How to walk your dog in the mountains with no magic leash
Sariel Har-Peled, Amir Nayyeri, Mohammad R. Salavatipour, Anastasios Sidiropoulos · 2012
We describe a O(log n)-approximation algorithm for computing the homotopic Frechet distance between two polygonal curves that lie on the boundary of a triangulated topological disk. Prior to this work, algorithms where known only for curves on the Euclidean plane with polygonal obstacles.