Abstract
Abstract Given art gallery with vertices, the maximum (sufficient) number of mobile guards is ⌊⌋ for simple polygon and ⌊⌋ for simple orthogonal polygon. However, there is no polynomial time algorithm for minimum number of mobile guards. This paper suggests polynomial time algorithm for the minimum number of mobile guards. Firstly, we obtain the visibility graph which is connected all edges if two vertices can be visible each other. Secondly, we select vertex with and with in and delete visible edges from and incident edges. Thirdly, we select in partial graphs and select edges that is the position of mobile guards. This algorithm applies various art galley problems with simple polygons and orthogonal polygons art gallery. As a results, the running time of proposed algorithm is linear time complexity and can be obtain the minimum number of mobile guards. Key Words : Art Gallery Problem, Polygon, Orthogonal Polygon, Stationary Guard, Mobile Guard
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