Let C be a simple 1 polygonal chain of n edges in the plane, and let p and q be two arbitrary points on C. The detour of C on (p,q) is defined to be the length of the subchain of C that connects p with q, divided by the Euclidean distance between p and q. Given an ε>0, we compute in time O(1/ ε nlogn) a pair of points on which the chain makes a detour at least 1/(1+ε) times the maximum detour. © 2003 Elsevier B.V.
Ebbers-Baumann, A., Klein, R., Langetepe, E., & Lingas, A. (2004). A fast algorithm for approximating the detour of a polygonal chain. Computational Geometry: Theory and Applications, 27(2), 123–134. https://doi.org/10.1016/S0925-7721(03)00046-4