Art gallery theorems and algorithms
Art gallery theorems and algorithms
Computational Geometry: Theory and Applications
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A polygon P is called k-vertex guardable if there is a subset G of the vertices of P such that each point in P is seen by at least k vertices in G. For the main results of this paper, it is shown that the following number of vertex guards is sufficient and sometimes necessary to k-vertex guard any simple n-gon P without holes: @?2n/3@? are needed for k=2 if P is any n-gon and @?3n/4@? are needed for k=3 if P is any convexly quadrilateralizable n-gon. The proofs for both of the results yield algorithms with O(n^2) runtimes.