Approximation Algorithms for Shortest Descending Paths in Terrains
  A path from s to t on a polyhedral terrain is descending if the height of a point p never increases while we move p along the path from s to t. No efficient algorithm is known to find a shortest descending path (SDP) from s to t in a polyhedral terrain. We give two approximation algorithms (more precisely, FPTASs) that solve the SDP problem on general terrains. Both algorithms are simple, robust and easy to implement. 
Mustaq Ahmed, Sandip Das, Sachin Lodha, Anna Lubiw, Anil Maheshwari,   Sasanka Roy