The Complexity of Guarding Monotone Polygons

A polygon P is x-monotone if any line orthogonal to the x-axis has a simply connected intersection with P. A set G of points inside P or on the boundary of P is said to guard the polygon if every point inside P or on the boundary of P is seen by a point in G. An interior guard can lie anywhere inside or on the boundary of the polygon. Using a reduction from Monotone 3SAT, we prove that the decision version of this problem is NP-hard. Because interior guards can be placed anywhere inside the polygon, a clever gadget is introduced that forces interior guards to be placed at very specific locations