Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Tuesday, November 08, 2011, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Andreas Bärtschi

Conflict-free art gallery coverage (master's thesis)

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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