Approximate shortest descent path on a terrain
Sasanka Roy, Sachin Lodha, Sandip Das, Anil Maheshwari · 2007
A path from a point s to a point t on the surface of a polyhedral terrain is said to be descent if for every pair of points p = (x(p),y(p),z(p)) and q = (x(q),y(q),z(q)) on the path, if dist(s,p) < dist(s,q) then z(p) ≥ z(q), where dist(s,p) denotes the distance of p from s along the aforesaid path. Although an efficient algorithm to decide if there is a descending path between two points is known for more than a decade, no efficient algorithm is yet known to find a shortest descending. In this paper we propose an (1 + ǫ)-approximation algorithm running in polynomial time for the same. 1