### Abstract

Original language | English |
---|---|

Pages (from-to) | 101-118 |

Number of pages | 18 |

Journal | Computational Geometry: Theory and Applications |

Volume | 68 |

DOIs | |

Publication status | Published - 2018 |

### Cite this

*Computational Geometry: Theory and Applications*,

*68*, 101-118. https://doi.org/10.1016/j.comgeo.2017.05.010

**Modem Illumination of Monotone Polygons.** / Aichholzer, Oswin; Fabila-Monroy, Ruy; Flores-Peñaloza, David; Hackl, Thomas; Urrutia Galicia, Jorge; Vogtenhuber, Birgit.

Research output: Contribution to journal › Article › Research › peer-review

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

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TY - JOUR

T1 - Modem Illumination of Monotone Polygons

AU - Aichholzer, Oswin

AU - Fabila-Monroy, Ruy

AU - Flores-Peñaloza, David

AU - Hackl, Thomas

AU - Urrutia Galicia, Jorge

AU - Vogtenhuber, Birgit

N1 - Special Issue in Memory of Ferran Hurtado

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

U2 - https://doi.org/10.1016/j.comgeo.2017.05.010

DO - https://doi.org/10.1016/j.comgeo.2017.05.010

M3 - Article

VL - 68

SP - 101

EP - 118

JO - Computational geometry

JF - Computational geometry

SN - 0925-7721

ER -