Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, August 24, 2010, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Csaba Dávid Tóth (University of Calgary)

Watchman Tours for Polygons with Holes

A watchman tour in a polygonal domain (for short, polygon) is a closed curve such that every point in the polygon is visible from at least one point of the tour. The problem of finding a shortest watchman tour is NP-hard for polygons with holes. We show that the length of a minimum watchman tour in a polygon P with k holes is O(per(P) + \sqrt{k}*diam(P)), where per(P) and diam(P) denote the perimeter and the diameter of P, respectively. Apart from the multiplicative constant, this bound is tight in the worst case. A watchman tour of this length can be computed in O(n\log n) time, where n is the total number of vertices. We generalize our results to watchman tours in polyhedra with holes in 3-space. We obtain an upper bound O(per(P) + \sqrt{k*per(P)*diam(P)} + k^{2/3}*diam(P)), which is again tight in the worst case.

Joint work with Adrian Dumitrescu.

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