On Conflict-Free Chromatic Guarding of Simple Polygons

Abstract

We study the problem of colouring the vertices of a polygon, such that every viewer can see a unique colour. The goal is to minimize the number of colours used. This is also known as the conflict-free chromatic guarding problem with vertex guards, and is motivated, e.g., by the problem of radio frequency assignment to sensors placed at the polygon vertices. We study the scenario in which viewers can be all points of the polygon (such as a mobile robot which moves in the interior of the polygon). We efficiently solve the related problem of minimizing the number of guards and approximate (up to only an additive error) the number of colours required in the special case of polygons called funnels. As a corollary we sketch an upper bound of colours on n-vertex weak visibility polygons which generalizes to all simple polygons.