Recent Results in Art Galleries

Two points in a polygon are called visible if the straight line segment between them lies entirely inside the polygon. The art gallery problem for a polygon P is to find a minimum set of points G in P such that every point of P is visible from some point of G. This problem has been shown to be NP-hard by Lee and Lin [71]. However, Chvatal showed that the number of points of G will never exceed [n/3] for a simple polygon of n sides [21]. This latter result is referred to as the art gallery theorem

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