Super Guarding and Dark Rays in Art Galleries
<|reference_start|>Super Guarding and Dark Rays in Art Galleries: We explore an Art Gallery variant where each point of a polygon must be seen by k guards, and guards cannot see through other guards. Surprisingly, even covering convex polygons under this variant is not straightforward. For example, covering every point in a triangle k=4 times (a 4-cover) requires 5 guards, and achieving a 10-cover requires 12 guards. Our main result is tight bounds on k-covering a convex polygon of n vertices, for all k and n. The proofs of both upper and lower bounds are nontrivial. We also obtain bounds for simple polygons, leaving tight bounds an open problem.<|reference_end|>
@article{mit compgeom group2024super,
    title={Super Guarding and Dark Rays in Art Galleries},
    author={MIT CompGeom Group, Hugo A. Akitaya, Erik D. Demaine, Adam Hesterberg,
  Anna Lubiw, Jayson Lynch, Joseph O'Rourke, Frederick Stock},
    journal={arXiv preprint arXiv:2404.04613},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.04613},
    primaryClass={cs.CG math.MG}
}