An Efficient Algorithm for Computing High-Quality Paths amid Polygonal Obstacles

We study a path-planning problem amid a set O of obstacles in R 2 , in which we wish to compute a short path between two points while also maintaining a high clearance from O; the clearance of a point is its distance from a nearest obstacle in O. Specifically, the problem asks for a path minimizing the reciprocal of the clearance integrated over the length of the path. We present the first polynomial-time approximation scheme for this problem....