Computational complexity of art gallery problems
IEEE Transactions on Information Theory
Art gallery theorems and algorithms
Art gallery theorems and algorithms
Computing
Approximation algorithms for NP-hard problems
Computational Geometry: Theory and Applications
Computing the shortest watchtower of a polyhedral terrain in O(nlogn) time
Computational Geometry: Theory and Applications
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Inapproximability Results for Guarding Polygons without Holes
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
Positioning Guards at Fixed Height Above a Terrain - An Optimum Inapproximability Result
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
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
Clique is hard to approximate within n1-
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Optimum Inapproximability Results for Finding Minimum Hidden Guard Sets in Polygons and Terrains
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
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
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How many people can hide in a given terrain, without any two of them seeing each other? We are interested in finding the precise number and an optimal placement of people to be hidden, given a terrain with n vertices. In this paper, we show that this is not at all easy: The problem of placing a maximum number of hiding people is almost as hard to approximate as the Maximum Clique problem, i.e., it cannot be approximated by any polynomial-time algorithm with an approximation ratio of nƐ for some Ɛ 0, unless P = NP. This is already true for a simple polygon with holes (instead of a terrain). If we do not allow holes in the polygon, we show that there is a constant Ɛ 0 such that the problem cannot be approximated with an approximation ratio of 1 + Ɛ.