English

Universal Guard Problems

Computational Geometry 2017-03-28 v2

Abstract

We provide a spectrum of results for the Universal Guard Problem, in which one is to obtain a small set of points ("guards") that are "universal" in their ability to guard any of a set of possible polygonal domains in the plane. We give upper and lower bounds on the number of universal guards that are always sufficient to guard all polygons having a given set of n vertices, or to guard all polygons in a given set of k polygons on an n-point vertex set. Our upper bound proofs include algorithms to construct universal guard sets of the respective cardinalities.

Keywords

Cite

@article{arxiv.1611.08315,
  title  = {Universal Guard Problems},
  author = {Sándor P. Fekete and Qian Li and Joseph S. B. Mitchell and Christian Scheffer},
  journal= {arXiv preprint arXiv:1611.08315},
  year   = {2017}
}

Comments

28 pages, 19 figures, full version of extended abstract that appeared in the 27th International Symposium on Algorithms and Computation (ISAAC 2016), 32:1-32:13

R2 v1 2026-06-22T17:03:49.245Z