Inapproximability Results for Guarding Polygons without Holes
نویسنده
چکیده
The three art gallery problems Vertex Guard, Edge Guard and Point Guard are known to be NP -hard [8]. Approximation algorithms for Vertex Guard and Edge Guard with a logarithmic ratio were proposed in [7]. We prove that for each of these problems, there exists a constant > 0, such that no polynomial time algorithm can guarantee an approximation ratio of 1 + unless P = NP . We obtain our results by proposing gap-preserving reductions, based on reductions from [8]. Our results are the first inapproximability results for these problems.
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