Universal guard problems

Given a set S of n points in the plane, how many universal guards are sometimes necessary and always sufficient to guard any simple polygon with vertex set S? We call this problem a Universal Guard Problem and provide a spectrum of results. We give upper and lower bounds on the number of universal guards that are always sufficient to guard all polygons having a given set of n vertices, or to guard all polygons in a given set of k polygons on an n-point vertex set. Our upper bound proofs include algorithms to construct universal guard sets of the respective cardinalities.