Abstract
AbstractRecently introduced in [1], the Chromatic Art Gallery Problem (CAGP) is related to the well known Art Gallery Problem to the extent that given a polygon P, a set of guards within P that satisfies a particular property is sought. Define a proper coloring of a guard set that covers the polygon as a color assignment in which any two guards receive different colors whenever their visibility regions intersect. The CAGP aims to find among the sets of guards that cover P one that admits a proper coloring of smallest cardinality. In this paper, we present an Integer Programming formulation for a discrete version of the CAGP and introduce techniques that allow us to attain proven optimal solutions for a variety of instances of the problem. Experiments were conducted considering vertex guards, but the method clearly works for any discrete set of guard candidates that guarantee full polygon coverage. Having been absent from the literature so far, experimental results are also discussed showing that this approach is of practical value.
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