In this paper we consider a variation of the Art Gallery Problem for orthogonal polygons. A set of points 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 in Pn is connected. The polygon P n 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. © Springer-Verlag 2003.
CITATION STYLE
Pinciu, V. (2003). Connected guards in orthogonal art galleries. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2669, 886–893. https://doi.org/10.1007/3-540-44842-x_90
Mendeley helps you to discover research relevant for your work.