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arXiv · 1503.05681

Combinatorics and complexity of guarding polygons with edge and point 2-transmitters

Sarah Cannon·Thomas G. Fai·Justin Iwerks·Undine Leopold·Christiane Schmidt
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Abstract

We consider a generalization of the classical Art Gallery Problem, where instead of a light source, the guards, called $k$-transmitters, model a wireless device with a signal that can pass through at most $k$ walls. We show it is NP-hard to compute a minimum cover of point 2-transmitters, point $k$-transmitters, and edge 2-transmitters in a simple polygon. The point 2-transmitter result extends to orthogonal polygons. In addition, we give necessity and sufficiency results for the number of edge 2-transmitters in general, monotone, orthogonal monotone, and orthogonal polygons.

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Sarah Cannon, Thomas G. Fai, Justin Iwerks, Undine Leopold, Christiane Schmidt. 2015-03-19. Combinatorics and complexity of guarding polygons with edge and point 2-transmitters. https://doi.org/10.1016/j.comgeo.2017.06.004

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