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
Art gallery theorems for guarded guards
Computational Geometry: Theory and Applications
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
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In this paper we consider a variation of the Art Gallery Problem for orthogonal polygons. A set of points G in a polygon Pn is a connected guard set for Pn provided that is a guard set and the visibility graph of the set of guards G in Pn is connected. The polygon Pn is orthogonal provided each interior angle is 90° or 270°. First we use a coloring argument to prove that the minimum number of connected guards which are necessary to watch any orthogonal polygon with n sides is n/2 - 2. This result was originally established by induction by Hernández-Peñalver. Then we prove a new result for art galleries with holes: we show that n/2 - h connected guards are always sufficient to watch an orthogonal art gallery with n walls and h holes. This result is sharp when n = 4h + 4. We also construct galleries that require at least n/2 - h - 1 connected guards, for all n and h.