Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

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

Duration: 30 minutes

Location: OAT S15/S16/S17

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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