A fast algorithm for approximating the detour of a polygonal chain
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 epsilon >0, we compute in time O((1)/(epsilon) n log n) a pair of points on which the chain makes a detour at least 1/(1 + epsilon) t
