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By Kurt (d-mpi-i) Sack and Jörg (d-mpi-i) Zaks


From the text: “In [I. Salleh, Comput. Geom. 42 (2009), no. 4, 352–361; MR2488875], the following results were shown: “‘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.’ “The purpose of this note is to show that these results admit a simple proof. Moreover, the positions of the guards can be computed in linear time, if a decomposition into triangles, respectivel

Year: 2013
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