## Energy Aware Stage Illumination

### Friedrich Eisenbrand, Stefan Funke, Andreas Karrenbauer, Domagoj Matijevic

Consider the following illumination problem: given a stage represented by
a line segment $\Stage$ 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. \cite{u-agip-00}) 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.

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