Modem Illumination of Monotone Polygons

Oswin Aichholzer, Ruy Fabila-Monroy, David Flores-Peñaloza, Thomas Hackl, Jorge Urrutia Galicia, Birgit Vogtenhuber

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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 languageEnglish
Pages (from-to)101-118
Number of pages18
JournalComputational Geometry
Publication statusPublished - 2018

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