Abstract
A sliding k-transmitter inside an orthogonal polygon P, for a fixed \(k\ge 0\), is a point guard that travels along an axis-parallel line segment s in P. The sliding k-transmitter can see a point \(p\in P\) if the perpendicular from p onto s intersects the boundary of P in at most k points. In the Minimum Sliding k-Transmitters (\({\hbox {ST}}_k\)) problem, the objective is to guard P with the minimum number of sliding k-transmitters. In this paper, we give a constant-factor approximation algorithm for the \({\hbox {ST}}_k\) problem on P for any fixed \(k\ge 0\). Moreover, we show that the \({\hbox {ST}}_0\) problem is NP-hard on orthogonal polygons with holes even if only horizontal sliding 0-transmitters are allowed. For \(k>0\), the problem is NP-hard even in the extremely restricted case where P is simple and monotone. Finally, we study art gallery theorems; i.e., we give upper and lower bounds on the number of sliding transmitters required to guard P relative to the number of vertices of P.
Published Version
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