A pedestrian approach to ray shooting: shoot a ray, take a walk
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
An Optimal Algorithm for Computing Visibility in the Plane
SIAM Journal on Computing
Efficient computation of query point visibility in polygons with holes
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Guarding galleries and terrains
Information Processing Letters
An Exact and Efficient Algorithm for the Orthogonal Art Gallery Problem
SIBGRAPI '07 Proceedings of the XX Brazilian Symposium on Computer Graphics and Image Processing
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
A nearly optimal sensor placement algorithm for boundary coverage
Pattern Recognition
An IP solution to the art gallery problem
Proceedings of the twenty-fifth annual symposium on Computational geometry
Visibility queries in a polygonal region
Computational Geometry: Theory and Applications
Experimental evaluation of an exact algorithm for the orthogonal art gallery problem
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
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The classical Art Gallery Problem asks for the minimum number of guards that achieve visibility coverage of a given polygon. This problem is known to be NP-hard, even for very restricted and discrete special cases. For the case of vertex guards and simple orthogonal polygons, Cuoto et al. have recently developed an exact method that is based on a set-cover approach. For the general problem (in which both the set of possible guard positions and the point set to be guarded are uncountable), neither constant-factor approximation algorithms nor exact solution methods are known. We present a primal-dual algorithm based on linear programming that provides lower bounds on the necessary number of guards in every step and—in case of convergence and integrality—ends with an optimal solution. We describe our implementation and give experimental results for an assortment of polygons, including nonorthogonal polygons with holes.