SCG '86 Proceedings of the second annual symposium on Computational geometry
An optimal algorithm for the two-guard problem
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Proceedings of the eleventh annual symposium on Computational geometry
Approximation algorithms for terrain guarding
Information Processing Letters
Optimum Inapproximability Results for Finding Minimum Hidden Guard Sets in Polygons and Terrains
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Illuminating Both Sides of Line Segments
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
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
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
Illumination of polygons by 45°-floodlights
Discrete Mathematics
Energy-aware stage illumination
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
On boundaries of highly visible spaces and applications
Theoretical Computer Science - Foundations of computation theory (FCT 2003)
Finding minimum hidden guard sets in polygons: tight approximability results
Computational Geometry: Theory and Applications
Approximating a Shortest Watchman Route
Fundamenta Informaticae
Computing the maximum clique in the visibility graph of a simple polygon
Journal of Discrete Algorithms
Maximizing the guarded boundary of an Art Gallery is APX-complete
Computational Geometry: Theory and Applications
Optimal and approximate approaches for deployment of heterogeneous sensing devices
EURASIP Journal on Wireless Communications and Networking
A General Method for Sensor Planning in Multi-Sensor Systems: Extension to Random Occlusion
International Journal of Computer Vision
On guarding the vertices of rectilinear domains
Computational Geometry: Theory and Applications
On Some City Guarding Problems
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Guarding Art Galleries: The Extra Cost for Sculptures Is Linear
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Improved Bounds for Wireless Localization
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Guarding curvilinear art galleries with vertex or point guards
Computational Geometry: Theory and Applications
An IP solution to the art gallery problem
Proceedings of the twenty-fifth annual symposium on Computational geometry
Minimum vertex guard problem for orthogonal polygons: a genetic approach
MAMECTIS'08 Proceedings of the 10th WSEAS international conference on Mathematical methods, computational techniques and intelligent systems
Efficient Viewpoint Selection for Urban Texture Documentation
GSN '09 Proceedings of the 3rd International Conference on GeoSensor Networks
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
Finding minimum hidden guard sets in polygons---tight approximability results
Computational Geometry: Theory and Applications
Planning motion in point-represented contact spaces using approximate star-shaped decomposition
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
Note: Approximation algorithms for art gallery problems in polygons
Discrete Applied Mathematics
maximizing the guarded boundary of an art gallery is APX-complete
CIAC'03 Proceedings of the 5th Italian conference on Algorithms and complexity
Approximation algorithms to minimum vertex cover problems on polygons and terrains
ICCS'03 Proceedings of the 1st international conference on Computational science: PartI
Computing multiple watchman routes
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Computational Geometry: Theory and Applications
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Algorithms and theory of computation handbook
Coverage with k-transmitters in the presence of obstacles
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Exploration strategies for a robot with a continously rotating 3D scanner
SIMPAR'10 Proceedings of the Second international conference on Simulation, modeling, and programming for autonomous robots
Visibility-based conformal cooling channel generation for rapid tooling
Computer-Aided Design
Proceedings of the twenty-seventh annual symposium on Computational geometry
SIAM Journal on Computing
On guarding rectilinear domains
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
How to place efficiently guards and paintings in an art gallery
PCI'05 Proceedings of the 10th Panhellenic conference on Advances in Informatics
Approximate guarding of monotone and rectilinear polygons
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Characterizing and covering some subclasses of orthogonal polygons
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
Approximation algorithms for art gallery problems in polygons and terrains
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
A 4-approximation algorithm for guarding 1.5-dimensional terrains
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Uninterrupted coverage of a planar region with rotating directional antennae
ADHOC-NOW'12 Proceedings of the 11th international conference on Ad-hoc, Mobile, and Wireless Networks
Approximating a Shortest Watchman Route
Fundamenta Informaticae
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
Fast vertex guarding for polygons with and without holes
Computational Geometry: Theory and Applications
Coverage with k-transmitters in the presence of obstacles
Journal of Combinatorial Optimization
Guarding thin orthogonal polygons is hard
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
Unsolved problems in visibility graphs of points, segments, and polygons
ACM Computing Surveys (CSUR)
| Hi-index | 754.84 |
We study the computational complexity of the art gallery problem originally posed by Klee, and its variations. Specifically, the problem of determining the minimum number of vertex guards that can see ann-wall simply connected art gallery is shown to be NP-hard. The proof can be modified to show that the problems of determining the minimum number of edge guards and the minimum number of point guards in a simply connected polygonal region are also NP-hard. As a byproduct, the problem of decomposing a simple polygon into a minimum number of star-shaped polygons such that their union is the original polygon is also shown to be NP-hard.