Art gallery theorem

The art gallery problem or museum problem is a well-studied visibility problem in computational geometry. It originates from a real-world problem of guarding an art gallery with the minimum number of guards who together can observe the whole gallery. In the computational geometry version of the problem the layout of the art gallery is represented by a simple polygon and each guard is represented by a point in the polygon. A set ${\displaystyle S}$ of points is said to guard a polygon if, for every point ${\displaystyle p}$ in the polygon, there is some ${\displaystyle q\in S}$ such that the line segment between ${\displaystyle p}$ and ${\displaystyle q}$ does not leave the polygon.

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