Computational geometry: an introduction
Computational geometry: an introduction
Optimal point location in a monotone subdivision
SIAM Journal on Computing
A pedestrian approach to ray shooting: shoot a ray, take a walk
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
The 2-center problem with obstacles
Proceedings of the sixteenth annual symposium on Computational geometry
Fast computation of smallest enclosing circle with center on a query line segment
Information Processing Letters
Constrained minimum enclosing circle with center on a query line segment
Computational Geometry: Theory and Applications
Largest empty circle centered on a query line
Journal of Discrete Algorithms
Some variations on constrained minimum enclosing circle problem
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Constrained minimum enclosing circle with center on a query line segment
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Approximating generalized distance functions on weighted triangulated surfaces with applications
Journal of Computational and Applied Mathematics
Some variations on constrained minimum enclosing circle problem
Journal of Combinatorial Optimization
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We develop efficient algorithms for locating an obnoxious facility in a simple polygonal region and for locating a desirable facility in a simple polygonal region. Many realistic facility location problems require the facilities to be constrained to lie in a simple polygonal region. Given a set S of m demand points and a simple polygon R of n vertices, we first show how to compute the location of an obnoxious facility constrained to lie in R, in O((m + n) logm + mlog n) time. We then show how to compute the location of a desirable facility constrained to lie in R, also in O((m + n) logm + mlog n) time. Both running times are an improvement over the known algorithms in the literature. Finally, our results generalize to the setting where the facility is constrained to lie within a set of simple polygons as opposed to a single polygon at a slight increase in complexity.