Guarding the granary

Guarding Art Galleries by Guarding Witnesses

Let P be a simple polygon. We define a witness set W to be a set of points such that if any (prospective) guard set G guards W , then it is guaranteed that G guards P . We show that not all polygons admit a finite witness set. If a finite minimal witness set exists, then it cannot contain any witness in the interior of P ; all witnesses must lie on the boundary of P , and there can be at most o...

Guarding the Body

Guarding the Gate

BACKGROUND Failed treatment trials are common in major depressive disorder and treatment-resistant depression, and remotely performed multifaceted, centralized structured interviews can potentially enhance signal detection by ensuring that enrolled patients meet eligibility criteria. METHODS We assessed the use of a specific remote structured interview that validated the diagnosis, level of t...

Triangle Guarding

We consider the problem of triangle guarding (4-guarding) a simple, 2D polygon Q. A polygon Q is 4-guarded if every point q of Q is contained in the convex hull of some three guards that can all see q. This rather odd condition approximates a desire, for example, to see all sides of q or to locate (via triangulation) q from at least two angularly well-separated views. If we restrict the guards ...

The Complexity of Guarding Terrains

A set G of points on a 1.5-dimensional terrain, also known as an x-monotone polygonal chain, is said to guard the terrain if any point on the terrain is seen by a point in G. Two points on the terrain see each other if and only if the line segment between them is never strictly below the terrain. The minimum terrain guarding problem asks for a minimum guarding set for the given input terrain. W...