Computational complexity of art gallery problems
IEEE Transactions on Information Theory
Art gallery theorems and algorithms
Art gallery theorems and algorithms
Some APX-completeness results for cubic graphs
Theoretical Computer Science
Complexity of approximating bounded variants of optimization problems
Theoretical Computer Science - Foundations of computation theory (FCT 2003)
On guarding the vertices of rectilinear domains
Computational Geometry: Theory and Applications
An “Art Gallery Theorem” for pyramids
Information Processing Letters
Note: Approximation algorithms for art gallery problems in polygons
Discrete Applied Mathematics
A nearly optimal algorithm for covering the interior of an Art Gallery
Pattern Recognition
Proceedings of the twenty-seventh annual symposium on Computational geometry
Approximate guarding of monotone and rectilinear polygons
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On the complexity of locating linear facilities in the plane
Operations Research Letters
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An orthogonal polygon of P is called "thin" if the dual graph of the partition obtained by extending all edges of P towards its interior until they hit the boundary is a tree. We show that the problem of computing a minimum guard set for either a thin orthogonal polygon or only its vertices is NP-hard, indeed APX-hard, either for guards lying on the boundary or on vertices of the polygon. For guards lying anywhere in the polygon, we show that computing an optimal guard set for the vertices of such a polygon is NP-hard.