Computational complexity of art gallery problems
IEEE Transactions on Information Theory
The problem of compatible representatives
SIAM Journal on Discrete Mathematics
Journal of the ACM (JACM)
Inapproximability Results for Guarding Polygons without Holes
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
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 1.5D Terrain Guarding
SIAM Journal on Computing
Minimum-weight triangulation is NP-hard
Journal of the ACM (JACM)
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
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
A pseudopolynomial time O(log n)-approximation algorithm for art gallery problems
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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A set G of points on a 1.5-dimensional terrain, also known as an x-monotone polygonal chain, is said to guard the terrain if every point on the terrain is seen by a point in G. Two points on the terrain see each other if and only if the line segment between them is never strictly below the terrain. The minimum terrain guarding problem asks for a minimum guarding set for the given input terrain. Using a reduction from PLANAR 3-SAT we prove that the decision version of this problem is NP-hard. This solves a significant open problem and complements recent positive approximability results for the optimization problem.