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.
This work is partially supported by the Swiss National Science Foundation
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© 1998 Springer-Verlag Berlin Heidelberg
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Eidenbenz, S. (1998). Inapproximability Results for Guarding Polygons without Holes. In: Chwa, KY., Ibarra, O.H. (eds) Algorithms and Computation. ISAAC 1998. Lecture Notes in Computer Science, vol 1533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49381-6_45
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DOI: https://doi.org/10.1007/3-540-49381-6_45
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