A system to place observers on a polyhedral terrain in polynomial time

The Art Gallery Problem deals with determining the number of observers necessary to cover an art gallery room such that every point is seen by at least one observer. This problem is well known and has a linear time solution for the 2 dimensional case, but little is known in the 3-D case. In this paper we present a polynomial time solution for the 3-D version of the Art Gallery Problem. Because the problem is NP-hard, the solution presented is an approximation, and we present the bounds to our solution. The solution uses techniques from i computational geometry to rst build a terrain hierarchy keeping the overall terrain's shape and to compute the visibility map for each observer, ii graph coloring to make a rst placement of observers on the terrain, and iii set coverage to reduce the number of observers based on their visibility map. A complexity analysis is presented for each step and an analysis of the overall quality of the solution is given.

• Type: Journal
• Year: 2000
• Where: IVC
• Authors: Maurício Marengoni, Bruce A. Draper, Allen R. Hanson, R. Sitaraman
• Keywords: Art Gallery, Art Gallery Problem, IVC 2000, Solution