Computational complexity of art gallery problems
IEEE Transactions on Information Theory
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximation algorithms for terrain guarding
Information Processing Letters
Positioning Guards at Fixed Height Above a Terrain - An Optimum Inapproximability Result
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Davenport--Schinzel Sequences and Their Geometric Applications
Davenport--Schinzel Sequences and Their Geometric Applications
The art gallery theorem: its variations, applications and algorithmic aspects
The art gallery theorem: its variations, applications and algorithmic aspects
Improved approximation algorithms for geometric set cover
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
A constant-factor approximation algorithm for optimal terrain guarding
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On guarding the vertices of rectilinear domains
Computational Geometry: Theory and Applications
Smoothing Imprecise 1.5D Terrains
Approximation and Online 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
Note: Approximation algorithms for art gallery problems in polygons
Discrete Applied Mathematics
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
SIAM Journal on Computing
Approximation algorithms for art gallery problems in polygons and terrains
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
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In the 1.5-dimensional terrain guarding problem we are given as input an x-monotone chain (the terrain) and asked for the minimum set of guards (points on the terrain) such that every point on the terrain is seen by at least one guard. It has recently been shown that the 1.5-dimensional terrain guarding problem is approximable to within a constant factor [3,7], though no attempt has been made to minimize the approximation factor. We give a 4-approximation algorithm for the 1.5D terrain guarding problem that runs in quadratic time. Our algorithm is faster, simpler, and has a better worst-case approximation factor than previous algorithms.