Conflict-Free Chromatic Art Gallery Coverage

We consider a chromatic variant of the art gallery problem, where each guard is assigned one of k distinct colors. A placement of such colored guards is conflict-free if each point of the polygon is seen by some guard whose color appears exactly once among the guards visible to that point. What is the smallest number k ( n ) of colors that ensure a conflict-free covering of all n -vertex polygons? We call this the conflict-free chromatic art gallery problem . Our main result shows that k ( n ) is O (log n ) for orthogonal and for monotone polygons, and O (log 2 n ) for arbitrary simple polygons. By contrast, if all guards visible from each point must have distinct colors, then k ( n ) is Ω ( n ) for arbitrary simple polygons, as shown by Erickson and LaValle (Robotics: Science and Systems, vol. VII, pp. 81–88, 2012 ). The problem is motivated by applications in distributed robotics and wireless sensor networks but is also of interest from a theoretical point of view.