Good Illumination of Minimum Range
<|reference_start|>Good Illumination of Minimum Range: A point p is 1-well illuminated by a set F of n point lights if p lies in the interior of the convex hull of F. This concept corresponds to triangle-guarding or well-covering. In this paper we consider the illumination range of the light sources as a parameter to be optimized. First, we solve the problem of minimizing the light sources' illumination range to 1-well illuminate a given point p. We also compute a minimal set of light sources that 1-well illuminates p with minimum illumination range. Second, we solve the problem of minimizing the light sources' illumination range to 1-well illuminate all the points of a line segment with an O(n^2) algorithm. Finally, we give an O(n^2 log n) algorithm for preprocessing the data so that one can obtain the illumination range needed to 1-well illuminate a point of a line segment in O(log n) time. These results can be applied to solve problems of 1-well illuminating a trajectory by approaching it to a polygonal path.<|reference_end|>
@article{abellanas2006good,
    title={Good Illumination of Minimum Range},
    author={M. Abellanas, A. Bajuelos, G. Hern'andez, F. Hurtado, I. Matos, B.
  Palop},
    journal={arXiv preprint arXiv:cs/0606013},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0606013},
    primaryClass={cs.CG}
}