Computational complexity of art gallery problems
IEEE Transactions on Information Theory
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
Modern computer algebra
Approximation algorithms for geometric shortest path problems
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Art gallery problem with guards whose range of vision is 180°
Computational Geometry: Theory and Applications
Allocating vertex π-guards in simple polygons via pseudo-triangulations
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
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Consider the following illumination problem: given a stage represented by a line segment L and a set of lightsources represented by a set of points S in the plane, assign powers to the lightsources such that every point on the stage receives a sufficient amount -- let's say one unit -- of light while minimizing the overall power consumption. By assuming that the amount of light arriving from a fixed lightsource decreases rapidly with the distance from the lightsource, this becomes an interesting optimization problem.We propose to reconsider the classical illumination problems as known from computational geometry literature (e.g. [12]) under this light attenuation model. This paper examines the simple problem introduced above and presents different solutions, based on convex optimization, discretization and linear programming, as well as a purely combinatorial approximation algorithm. Some experimental results are also provided.