- Journal Article
Rights / licenseIn Copyright - Non-Commercial Use Permitted
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(logn) for orthogonal and for monotone polygons, and O(log2 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. Show more
Journal / seriesAlgorithmica
Pages / Article No.
SubjectArt gallery problem; Conflict-free coloring; Visibility; Polygon partitioning
Organisational unit03340 - Widmayer, Peter / Widmayer, Peter
03457 - Welzl, Emo / Welzl, Emo
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Is referenced by: https://doi.org/10.3929/ethz-b-000074425
NotesIt was possible to publish this article open access thanks to a Swiss National Licence with the publisher.
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