# Stage Illumination Problem

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Consider the following illumination problem: given a stage represented by a horizontal line segment and a set of light sources represented by a set of points in the plane above, assign powers to the light sources such that every point on the stage receives a sufficient amount (say one unit) of light while minimizing the overall power consumption. Under the assumption that the amount of light arriving from a fixed light source decreases rapidly with the distance from the light source, this becomes an interesting optimization problem. Two approximation algorithms based on linear programming are used in this Demonstration.

Contributed by: Slobodan Jelic and Domagoj Matijevic (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Two approximation algorithms implemented in this Demonstration are based on the following article:

F. Eisenbrand, S. Funke, A. Karrenbauer, and D. Matijevic, "Energy-Aware Stage Illumination," *International Journal of Computational Geometry and Applications*, 18, 2008 pp. 107–129.

## Permanent Citation

"Stage Illumination Problem"

http://demonstrations.wolfram.com/StageIlluminationProblem/

Wolfram Demonstrations Project

Published: March 7 2011