Art gallery theorems and algorithms
Art gallery theorems and algorithms
An optimal algorithm to solve the minimum weakly cooperative guards problem for 1-spiral polygons
Information Processing Letters
Multiply Guarded Guards in Orthogonal Art Galleries
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
Cooperative mobile guards in grids
Computational Geometry: Theory and Applications
Guarding Art Galleries: The Extra Cost for Sculptures Is Linear
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Connected guards in orthogonal art galleries
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
A coloring algorithm for finding connected guards in art galleries
DMTCS'03 Proceedings of the 4th international conference on Discrete mathematics and theoretical computer science
An efficient algorithm for mobile guarded guards in simple grids
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
How Ants Can Efficiently Solve Generalized Watchman Route Problem
International Journal of Swarm Intelligence Research
| Hi-index | 0.00 |
We prove two art gallery theorems in which the guards must guard one another in addition to the gallery. A set G of points (the guards) in a simple closed polygon (the art gallery) is a guarded guard set provided (i) every point in the polygon is visible to some point in G; and (ii) every point in G is visible to some other point in G. We prove that a polygon with n sides always has a guarded guard set of cardinality ⌊(3n - 1)/7⌋ and that this bound is sharp (n ≥ 5); our result corrects an erroneous formula in the literature. We also use a coloring argument to give an entirely new proof that the corresponding sharp function for orthogonal polygons is ⌊n/3⌋ for n ≥ 6; this result was originally established by induction by Hernández-Peñalver.