**Papers Published**

- Agarwal, PK; Fox, K; Salzman, O,
*An efficient algorithm for computing high-quality paths amid polygonal obstacles*, Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 2 (January, 2016), pp. 1179-1192, ISBN 9781510819672

(last updated on 2018/12/10)**Abstract:**

© Copyright (2016) by SIAM: Society for Industrial and Applied Mathematics. We study a path-planning problem amid a set 0 of obstacles in R2, in which we wish to compute a short path between two points while also maintaining a high clearance from 0; the clearance of a point is its distance from a nearest obstacle in 0. 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 0(n2/ϵ2 log n/ϵ) a path of total cost at most (1 + ϵ) times the cost of the optimal path.