Computational complexity of art gallery problems
IEEE Transactions on Information Theory
Allocating Vertex π-Guards in Simple Polygons via Pseudo-Triangulations
Discrete & Computational Geometry
Computational geometry column 48
ACM SIGACT News
Guard placement for efficient point-in-polygon proofs
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Maximizing the guarded boundary of an Art Gallery is APX-complete
Computational Geometry: Theory and Applications
Coverage with k-transmitters in the presence of obstacles
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Coverage with k-transmitters in the presence of obstacles
Journal of Combinatorial Optimization
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We consider a novel class of art gallery problems inspired by wireless localization. Given a simple polygon P, place and orient guards each of which broadcasts a unique key within a fixed angular range. Broadcasts are not blocked by the edges of P. The interior of the polygon must be described by a monotone Boolean formula composed from the keys. We improve both upper and lower bounds for the general setting by showing that the maximum number of guards to describe any simple polygon on nvertices is between roughly ${\frac{3}{5}}$n and $\frac{4}{5}$n. For the natural setting where guards may be placed aligned to one edge or two consecutive edges of Ponly, we prove that n茂戮驴 2 guards are always sufficient and sometimes necessary.