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http://dx.doi.org/10.7236/JIWIT.2012.12.3.63

The Minimum number of Mobile Guards Algorithm for Art Gallery Problem  

Lee, Sang-Un (Dept. of Multimedia Engineering, Gangnung-Wonju National University Wonju Campus)
Choi, Myeong-Bok (Dept. of Multimedia Engineering, Gangnung-Wonju National University Wonju Campus)
Publication Information
The Journal of the Institute of Internet, Broadcasting and Communication / v.12, no.3, 2012 , pp. 63-69 More about this Journal
Abstract
Given art gallery P with n vertices, the maximum (sufficient) number of mobile guards is${\lfloor}n/4{\rfloor}$ for simple polygon and${\lfloor}(3n+4)/16{\rfloor}$ 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 u with ${\Delta}(G)$ and v with ${\Delta}(G)$ in $N_G(u)$ and delete visible edges from u,v and incident edges. Thirdly, we select $w_i$ 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.
Keywords
Art Gallery Problem; Polygon; Orthogonal Polygon; Stationary Guard; Mobile Guard;
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