Optimal obnoxious paths on a network: transportation of hazardous materials
Operations Research
Pattern Recognition Letters
A simple on-line randomized incremental algorithm for computing higher order Voronoi diagrams
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Applications of parametric searching in geometric optimization
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
Widest empty L-shaped corridor
Information Processing Letters
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Computational geometry in C (2nd ed.)
Computational geometry in C (2nd ed.)
Nordic Journal of Computing
On k-Nearest Neighbor Voronoi Diagrams in the Plane
IEEE Transactions on Computers
Computing an obnoxious anchored segment
Operations Research Letters
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Given a set of n points S in the Euclidean plane, we address the problem of computing an annulus A, (open region between two concentric circles) of largest width such that no point p 驴 S lies in the interior of A. This problem can be considered as a minimax facility location problem for n points such that the facility is a circumference. We give a characterization of the centres of annuli which are locally optimal and we show the the problem can be solved in O(n3 log n) time and O(n) space. We also consider the case in which the number of points in the inner circle is a fixed value k. When k 驴 O(n) our algorithm runs in O(n3 log n) time and O(n) space. However if k is small, that is a fixed constant, we can solve the problem in O(n log n) time and O(n) space.