A Novel Efficient Approach for Solving the Art Gallery Problem
In this paper, we consider the Art Gallery Problem (AGP) that asks for the minimum number of guards placed in a polygon to oversee the whole polygon. The AGP is known to be NP-hard even for very restricted special cases. This paper describes a primal-dual algorithm based on continuous optimization techniques for solving large-scale instances of the Art Gallery Problem. More precisely, the algorithm is a combination of methods from computational geometry, linear programming (LP), and Difference of Convex functions (DC) programming. The structure of the algorithm permits to provide lower and upper bounds on the minimum number of guards. In order to evaluate the algorithm, we measure its performance by solving some standard test instances including some non-orthogonal polygons with holes.
KeywordsArt Gallery Problem Linear Programming DC Programming Duality Separation Visibility
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