Prof. Emo Welzl and Prof. Bernd Gärtner
|Mittagsseminar Talk Information|
Date and Time: Tuesday, November 08, 2011, 12:15 pm
Duration: 30 minutes
Location: CAB G51
Speaker: Andreas Bärtschi
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 coloring 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.
Advisors: S. Suri (UCSB), E. Welzl (ETHZ)
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