Art gallery theorems and algorithms
Art gallery theorems and algorithms
A threshold of ln n for approximating set cover (preliminary version)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Computational Geometry: Theory and Applications
Computing the shortest watchtower of a polyhedral terrain in O(nlogn) time
Computational Geometry: Theory and Applications
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
Inapproximability Results for Guarding Polygons without Holes
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
How Many People Can Hide in a Terrain?
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
On the Planar Two-Watchtower Problem
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
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
Budget Constrained Minimum Cost Connected Medians
WG '00 Proceedings of the 26th International Workshop on Graph-Theoretic Concepts in Computer Science
A 4-approximation algorithm for guarding 1.5-dimensional terrains
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
| Hi-index | 0.00 |
We study the problem of minimizing the number of guards positioned at a fixed height h such that each triangle on a given 2.5- dimensional triangulated terrain T is completely visible from at least one guard. We prove this problem to be NP-hard, and we show that it cannot be approximated by a polynomial time algorithm within a ratio of (1 - ∈) 1/35 ln n for any ∈ 0, unless NP ⊆ TIME (nO(log log n)), where n is the number of triangles in the terrain. Since there exists an approximation algorithm that achieves an approximation ratio of ln n+1, our result is close to the optimum hardness result achievable for this problem.