Abstract.
Consider an art gallery formed by a polygon on n vertices with m pairs of vertices joined by interior diagonals, the interior walls. Each interior wall has an arbi- trarily placed, arbitrarily small doorway. We show that the minimum number of guards that suffice to guard all art galleries with n vertices and m interior walls is \(\min\{ \lfloor (2n-3)/3\rfloor\) , \(\lfloor (2n+m-2)/4\rfloor, \lfloor (2m+n)/3\rfloor\}.\) If we restrict ourselves to galleries with convex rooms of size at least r , the answer improves to \(\min\{m,\lfloor{(n+m)/r}\rfloor.\}\) The proofs lead to linear time guard placement algorithms in most cases.
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Received September 1, 1997, and in revised form May 27, 1998.
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Kündgen, A. Art Galleries with Interior Walls. Discrete Comput Geom 22, 249–258 (1999). https://doi.org/10.1007/PL00009458
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DOI: https://doi.org/10.1007/PL00009458