Computational complexity of art gallery problems
IEEE Transactions on Information Theory
Art gallery theorems and algorithms
Art gallery theorems and algorithms
Optimization, approximation, and complexity classes
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Introduction to the theory of complexity
Introduction to the theory of complexity
Approximation algorithms for NP-hard problems
Computational Geometry: Theory and Applications
Positioning Guards at Fixed Height Above a Terrain - An Optimum Inapproximability Result
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
How Many People Can Hide in a Terrain?
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
MAXIMUM CLIQUE and MINIMUM CLIQUE PARTITION in Visibility Graphs
TCS '00 Proceedings of the International Conference IFIP on Theoretical Computer Science, Exploring New Frontiers of Theoretical Informatics
An Approximation Algorithm for MINIMUM CONVEX COVER with Logarithmic Performance Guarantee
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
An Approximation Scheme for Terrain Guarding
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
SIAM Journal on Computing
How to place efficiently guards and paintings in an art gallery
PCI'05 Proceedings of the 10th Panhellenic conference on Advances in Informatics
Approximate guarding of monotone and rectilinear polygons
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Fast vertex guarding for polygons with and without holes
Computational Geometry: Theory and Applications
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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 Ɛ 0, such that no polynomial time algorithm can guarantee an approximation ratio of 1 + Ɛ 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.