
Open access
Date
2014-01Type
- Journal Article
Citations
Cited 2 times in
Web of Science
Cited 12 times in
Scopus
ETH Bibliography
yes
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Abstract
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
Permanent link
https://doi.org/10.3929/ethz-b-000076373Publication status
publishedExternal links
Journal / series
AlgorithmicaVolume
Pages / Article No.
Publisher
SpringerSubject
Art gallery problem; Conflict-free coloring; Visibility; Polygon partitioningOrganisational unit
03340 - Widmayer, Peter / Widmayer, Peter
03457 - Welzl, Emo / Welzl, Emo
Related publications and datasets
Is referenced by: https://doi.org/10.3929/ethz-b-000074425
Notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.More
Show all metadata
Citations
Cited 2 times in
Web of Science
Cited 12 times in
Scopus
ETH Bibliography
yes
Altmetrics