Computational Complexity of the \(r\)-visibility Guard Set Problem for Polyominoes
We study the art gallery problem when the instance is a polyomino, which is the union of connected unit squares. It is shown that locating the minimum number of guards with \(r\)-visibility in a polyomino with holes is NP-hard. Here, two points \(u\) and \(v\) on a polyomino are r-visible if the orthogonal bounding rectangle for \(u\) and \(v\) lies entirely within the polyomino. As a corollary, locating the minimum number of guards with \(r\)-visibility in an orthogonal polygon with holes is NP-hard.
KeywordsArt gallery problem Polyomino \(r\)-visibility NP-hard
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