Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Farthest neighbors and center points in the presence of rectngular obstacles
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Quickest paths, straight skeletons, and the city Voronoi diagram
Proceedings of the eighteenth annual symposium on Computational geometry
CATS '07 Proceedings of the thirteenth Australasian symposium on Theory of computing - Volume 65
The transportation metric and related problems
Information Processing Letters
Optimal construction of the city voronoi diagram
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
A unified algorithm for continuous monitoring of spatial queries
DASFAA'11 Proceedings of the 16th international conference on Database systems for advanced applications: Part II
| Hi-index | 0.00 |
We consider the problem of computing all farthest neighbors (and the diameter) of a given set of n points in the presence of highways and obstacles in the plane. When traveling on the plane, travelers may use highways for faster movement and must avoid all obstacles. We present an efficient solution to this problem based on knowledge from earlier research on shortest path computation. Our algorithms run in $\ensuremath{O(nm(\log m + \log^2n))}$ time using O (m + n ) space, where the m is the combinatorial complexity of the environment consisting of highways and obstacles.