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Polygon decomposition and the orthogonal art gallery problem. (English) Zbl 1144.65015

It is NP-dard to find the minimum number of guards to watch the interior of an \(n\)-wall art gallery. However, if the guards have a restricted form of visibility, the problem may change its complexity. In this paper, the authors consider the problem about \(r\)-visibility. Two points \(p\) and \(q\) are \(r\)-visible if the orthogonal bounding rectangle for \(p\) and \(q\) lies within a given rectilinear polygon \(P\). The authors showed a polynomial-time algorithm to find the minimum number of guards with \(r\)-visibility to watch a rectilinear polygon.

MSC:

65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
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