Art gallery theorems and algorithms
Art gallery theorems and algorithms
Computational Geometry: Theory and Applications
A randomized art-gallery algorithm for sensor placement
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Approximation algorithms for terrain guarding
Information Processing Letters
On finding a guard that sees most and a shop that sells most
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Improved approximation algorithms for geometric set cover
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Guarding a terrain by two watchtowers
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
On guarding the vertices of rectilinear domains
Computational Geometry: Theory and Applications
Computing visibility on terrains in external memory
Journal of Experimental Algorithmics (JEA)
Epsilon nets and union complexity
Proceedings of the twenty-fifth annual symposium on Computational geometry
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
Weighted geometric set cover via quasi-uniform sampling
Proceedings of the forty-second ACM symposium on Theory of computing
Hitting sets online and vertex ranking
ESA'11 Proceedings of the 19th European conference on Algorithms
On guarding rectilinear domains
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Approximate guarding of monotone and rectilinear polygons
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
A 4-approximation algorithm for guarding 1.5-dimensional terrains
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Efficient algorithms for pursuing moving evaders in terrains
Proceedings of the 20th International Conference on Advances in Geographic Information Systems
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We present the first constant-factor approximation algorithm for a non-trivial instance of the optimal guarding (coverage) problem in polygons. In particular, we give an O(1)-approximation algorithm for placing the fewest point guards on a 1.5D terrain, so that every point of the terrain is seen by at least one guard. While polylogarithmic-factor approximations follow from set cover results, our new results exploit geometric structure of terrains to obtain a substantially improved approximation algorithm.