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arXiv · 2007.08368

Shortest Watchman Tours in Simple Polygons under Rotated Monotone Visibility

Bengt J. Nilsson·David Orden·Leonidas Palios·Carlos Seara·Paweł Żyliński
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Abstract

We present an $O(nrG)$ time algorithm for computing and maintaining a minimum length shortest watchman tour that sees a simple polygon under monotone visibility in direction $\theta$, while $\theta$ varies in $[0,180^{\circ})$, obtaining the directions for the tour to be the shortest one over all tours, where $n$ is the number of vertices, $r$ is the number of reflex vertices, and $G\leq r$ is the maximum number of gates of the polygon used at any time in the algorithm.

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Bengt J. Nilsson, David Orden, Leonidas Palios, Carlos Seara, Paweł Żyliński. 2020-07-16. Shortest Watchman Tours in Simple Polygons under Rotated Monotone Visibility. https://doi.org/10.1007/978-3-030-58150-3_25

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