Abstract
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.KeywordsLine SegmentApproximation AlgorithmVariable PatternPolynomial Time AlgorithmInapproximability ResultThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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