Widest empty L-shaped corridor
Information Processing Letters
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Modeling of Transport Risk for Hazardous Materials
Operations Research
Approximation of Point Sets by 1-Corner Polygonal Chains
INFORMS Journal on Computing
Semi-obnoxious single facility location in Euclidean space
Computers and Operations Research
Computing an obnoxious anchored segment
Operations Research Letters
On finding a widest empty 1-corner corridor
Information Processing Letters
On finding widest empty curved corridors
Computational Geometry: Theory and Applications
Improved algorithm for the widest empty 1-corner corridor
Information Processing Letters
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We consider an obnoxious facility location problem in which the facility is a trajectory consisting of a bounded length polygonal chain of two edges having extremes anchored at two given points. In other words, given a set S of points in the plane and a positive value l0, we want to compute an anchored 1-comer polygonal chain having length at most l0 such that the minimum distance to the points in S is maximized. We present non-trivial algorithms based on geometric properties of each possible configuration providing a solution. More specifically, we give an O(n log n)-time algorithm for finding a 1-corner obnoxious polygonal chain whose length is exactly l0, and an O(n2)-time algorithm when the length of the optimal chain is at most the given bound l0.