Computational complexity of art gallery problems
IEEE Transactions on Information Theory
Art gallery theorems and algorithms
Art gallery theorems and algorithms
Almost optimal set covers in finite VC-dimension: (preliminary version)
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
The Robot Localization Problem
SIAM Journal on Computing
Nice point sets can have nasty Delaunay triangulations
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
A randomized art-gallery algorithm for sensor placement
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Dense point sets have sparse Delaunay triangulations: or "…but not too nasty"
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Guarding galleries and terrains
Information Processing Letters
Guarding Art Galleries: The Extra Cost for Sculptures Is Linear
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
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
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
Fast vertex guarding for polygons with and without holes
Computational Geometry: Theory and Applications
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In this paper, we give a O(log copt)-approximation algorithm for the point guard problem where copt is the optimal number of guards. Our algorithm runs in time polynomial in n, the number of walls of the art gallery and the spread Δ, which is defined as the ratio between the longest and shortest pairwise distances. Our algorithm is pseudopolynomial in the sense that it is polynomial in the spread Δ as opposed to polylogarithmic in the spread Δ, which could be exponential in the number of bits required to represent the vertex positions. The special subdivision procedure in our algorithm finds a finite set of potential guard-locations such that the optimal solution to the art gallery problem where guards are restricted to this set is at most 3copt. We use a set cover cum VC-dimension based algorithm to solve this restricted problem approximately.