The art gallery problem is to determine the number of guards that are sufficient to cover or see every point in the interior of an art gallery. An art gallery can be viewed as a polygon P with or without holes with a total of n vertices and guards as points in P . Any point z ∈ P is said to be visible from a guard g if the line segment joining z and g does not intersect the exterior of P . Usually the guards may be placed anywhere inside P . If the guards are restricted to vertices of P , we call them vertex guards. If there is no restriction, the guards are referred as point guards. Point and vertex guards are also referred as stationary guards. If the guards are mobile, i.e., able to patrol along a segment inside P , they are called mobile guards. If the mobile guards are restricted to edges of P , they are called edge guards.