Sliding k-Transmitters: Hardness and Approximation

Sliding k-Transmitters: Hardness and Approximation

A sliding k-transmitter in an orthogonal polygon P is a mobile guard that travels back and forth along an orthogonal line segment s inside P. It can see a point p in P if the perpendicular from p onto s intersects the boundary of P at most k times. We show that guarding an orthogonal polygon P with...

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Veröffentlicht in:arXiv.org 2016-07
Hauptverfasser: Biedl, Therese, Mehrabi, Saeed, Yu, Ziting
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Algorithms
Approximation
Mathematical analysis
Sliding
Transmitters
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description A sliding k-transmitter in an orthogonal polygon P is a mobile guard that travels back and forth along an orthogonal line segment s inside P. It can see a point p in P if the perpendicular from p onto s intersects the boundary of P at most k times. We show that guarding an orthogonal polygon P with the minimum number of k-transmitters is NP-hard, for any fixed k>0, even if P is simple and monotone. Moreover, we give an O(1)-approximation algorithm for this problem.
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subjects Algorithms
Approximation
Mathematical analysis
Sliding
Transmitters
title Sliding k-Transmitters: Hardness and Approximation
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