Computational complexity of art gallery problems
IEEE Transactions on Information Theory
Computing
Approximating the minimum maximal independence number
Information Processing Letters
Approximation algorithms for NP-hard problems
Selected papers from the 12th annual symposium on Computational Geometry
Inapproximability of finding maximum hidden sets on polygons and terrains
Computational Geometry: Theory and Applications
Approximation algorithms for terrain guarding
Information Processing Letters
Digital Elevation Models and TIN Algorithms
Algorithmic Foundations of Geographic Information Systems, this book originated from the CISM Advanced School on the Algorithmic Foundations of Geographic Information Systems
Approximate guarding of monotone and rectilinear polygons
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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We study the problem Minimum Hidden Guard Set, which consists of positioning a minimum number of guards in a given polygon (or other structure such as a terrain) such that no two guards see each other and such that every point in the polygon is visible from at least one guard. By constructing a gap-creating reduction from 5-Occurrence-3-Satisfiability, we show that this problem cannot be approximated by any polynomial-time algorithm with an approximation ratio of |I|^1^-^@e for any @e0, unless NP=P, where |I| is the size of the input polygon. The result even holds for input polygons without holes, which separates the problem from other visibility problems such as guarding and hiding, where strong inapproximability results hold only for polygons with holes. We also show that a straight-forward approximation algorithm achieves an approximation ratio of |I|. These two results characterize the approximability threshold of Minimum Hidden Guard Set exactly up to low-order terms.