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Abstract:
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.
