The class of Art Gallery Problems is one of the very fascinating areas of computational geometry.

Imagine the floor plan of an art gallery as a two dimensional polygon with n vertices.
In 1973, Klee posed the initial question:

"How many stationary guards are needed to guard the room?"
In particular, Klee was referring to theoretical guards who were stationed at fixed points and had the ability to keep watch in all directions around themselves simultaneously.  This initial question opened up a whole class of similar problems all dealing with visibility.  The variations deal within polygons of varying complexity and guards of varying power.
 

Here you will find a discussion and further background history for art gallery theorems, some results for simple variants, and ultimately edge-guarding and mobile-guarding in simple polygons.



 
 
 
  

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