TY - GEN
T1 - An efficient algorithm for computing high-quality paths amid polygonal obstacles
AU - Agarwal, Pankaj K.
AU - Fox, Kyle
AU - Salzman, Oren
N1 - Funding Information: Work by P.A. and K.F. has been supported in part by NSF under grants CCF-09-40671, CCF-10-12254, CCF-11-61359, IIS-14-08846, and CCF-15-13816, and by Grant 2012/229 from the U.S.-Israel Binational Science Foundation. Work by O.S. has been supported in part by the Israel Science Foundation (grant no.1102/11), by the German-Israeli Foundation (grant no. 1150-82.6/2011), and by the Hermann Minkowski-Minerva Center for Geometry at Tel Aviv University.%blankline% Publisher Copyright: © Copyright (2016) by SIAM: Society for Industrial and Applied Mathematics.
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/84963656376
U2 - 10.1137/1.9781611974331.ch82
DO - 10.1137/1.9781611974331.ch82
M3 - Conference contribution
T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
SP - 1179
EP - 1192
BT - 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016
A2 - Krauthgamer, Robert
T2 - 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016
Y2 - 10 January 2016 through 12 January 2016
ER -