Abstract
The Art Gallery Problem (AGP) is one of the classic problems in Computational Geometry. For a given art gallery, represented by a polygon, the AGP seeks for the minimum number of guards that are necessary for overseeing the entire polygon. Many variants of this problems have already been studied. In this paper, we are interested in examining and visualizing two algorithms for the distributed version of the AGP, where guards are autonomous and have limited communication abilities. For this purpose, we present a self-contained simulator that is able to read or generate non convex polygons and to simulate the movements of robotic guards inside the polygonal environment by using the navigation algorithms. In particular, we study two algorithms: Random Search (RS) and Depth-First Search (DFS). We compare RS and DFS, in terms of computation time, by testing them on benchmark instances as well as randomly generated polygons. According to our experiments, each algorithm has a better performance on specific types of polygons.
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