Conflict-free chromatic art gallery coverage
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Date
2014-01
Publication Type
Journal Article
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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.
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published
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Journal / series
Volume
68 (1)
Pages / Article No.
265 - 283
Publisher
Springer
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Subject
Art gallery problem; Conflict-free coloring; Visibility; Polygon partitioning
Organisational unit
03457 - Welzl, Emo (emeritus) / Welzl, Emo (emeritus)
03340 - Widmayer, Peter (emeritus) / Widmayer, Peter (emeritus)
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It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.
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