A coloring algorithm for finding connected guards in art galleries

Authors:
Val Pinciu
Affiliations:
Mathematics Department, Southern Connecticut State University, New Haven, CT
Venue:
DMTCS'03 Proceedings of the 4th international conference on Discrete mathematics and theoretical computer science
Year:
2003

Citing 4
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Abstract

In this paper we consider a variation of the Art Gallery Problem. 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. We use a coloring argument to prove that the minimum number of connected guards which are necessary to watch any polygon with n sides is ⌊(n - 2)/2⌋. This result was originally established by induction by Hernández-Peñalver [3]. From this result it easily follows that if the art gallery is orthogonal (each interior angle is 90° or 270°), then the minimum number of connected guards is n/2 - 2.