Figure 11 shows an example of using string-pulling to smooth out the path. Let P be the path and N be the number of nodes on P. A new path is generated by removing any P i (P i is the Ith node from the starting node P 1 ) from P when it is possible to get from P i-1 to P i+1 directly. A smoother path is given after string-pulling but it still may not be the shortest path. An
explanation for the failure to find the shortest path may be that string-pulling as a post-processing technique only optimizes the path itself rather than the way to find the path.