**Papers Published**

- Agarwal, PK; Kyle, FOX; Salzman, O,
*An efficient algorithm for computing high-quality paths amid polygonal obstacles*, Acm Transactions on Algorithms, vol. 14 no. 4 (August, 2018), pp. 1-21, Association for Computing Machinery (ACM)

(last updated on 2019/05/22)**Abstract:**

© 2018 ACM. We study a path-planning problem amid a set O of obstacles in R2, 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. Let n be the total number of obstacle vertices and let ε ∈ (0, 1]. Our algorithm computes in time O(nε22 lognε ) a path of total cost at most (1 + ε) times the cost of the optimal path.