### Abstract

We study a generalization of the classical problem of illumination of polygons. Instead of modeling a light source we model a wireless device whose radio signal can penetrate a given number $k$ of walls. We call these objects $k$-modems and study the minimum number of $k$-modems necessary to illuminate monotone and monotone orthogonal polygons. We show that every monotone polygon on $n$ vertices can be illuminated with $leftlceil n2k right $k$-modems and exhibit examples of monotone polygons requiring $leftlceil n2k+2 right $k$-modems. For monotone orthogonal polygons, we show that every such polygon on $n$ vertices can be illuminated with $leftlceil n2k+4 right $k$-modems and give examples which require $leftlceil n2k+4 right $k$-modems for $k$ even and $leftlceil n2k+6 right for $k$ odd.

Original language | English |
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Pages (from-to) | 101-118 |

Number of pages | 18 |

Journal | Computational Geometry: Theory and Applications |

Volume | 68 |

DOIs | |

Publication status | Published - 2018 |

## Cite this

Aichholzer, O., Fabila-Monroy, R., Flores-Peñaloza, D., Hackl, T., Urrutia Galicia, J., & Vogtenhuber, B. (2018). Modem Illumination of Monotone Polygons.

*Computational Geometry: Theory and Applications*,*68*, 101-118. https://doi.org/10.1016/j.comgeo.2017.05.010