Guarding galleries and terrains

Authors:
Alon Efrat;Sariel Har-Peled
Affiliations:
Department of Computer Science, University of Arizona;Department of Computer Science, University of Illinois, Urbana, IL
Venue:
Information Processing Letters
Year:
2006

Citing 16
Cited 15

Art gallery theorems and algorithms

Art gallery theorems and algorithms
On the rectilinear art gallery problem

Proceedings of the seventeenth international colloquium on Automata, languages and programming
The Art Gallery theorem for polygons with holes

SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Generalized hidden surface removal

SCG '93 Proceedings of the ninth annual symposium on Computational geometry
An art gallery theorem for line segments in the plane

Pattern Recognition Letters - Special issue on computational geometry
Variations on the art gallery theorem

Variations on the art gallery theorem
On the combinatorial and algebraic complexity of quantifier elimination

Journal of the ACM (JACM)
On the bit complexity of minimum link paths: superquadratic algorithms for problems solvable in linear time

Proceedings of the twelfth annual symposium on Computational geometry
Computational geometry: algorithms and applications

Computational geometry: algorithms and applications
An output sensitive algorithm for discrete convex hulls

Computational Geometry: Theory and Applications
A randomized art-gallery algorithm for sensor placement

SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Covering shapes by ellipses

SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for terrain guarding

Information Processing Letters
Algorithms for Polytope Covering and Approximation

WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Guarding Galleries and Terrains

TCS '02 Proceedings of the IFIP 17th World Computer Congress - TC1 Stream / 2nd IFIP International Conference on Theoretical Computer Science: Foundations of Information Technology in the Era of Networking and Mobile Computing
The art gallery theorem: its variations, applications and algorithmic aspects

The art gallery theorem: its variations, applications and algorithmic aspects

A nearly optimal sensor placement algorithm for boundary coverage

Pattern Recognition
A new lower bound for evaluating the performances of sensor location algorithms

Pattern Recognition Letters
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
Minimum Covering with Travel Cost

ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Note: Approximation algorithms for art gallery problems in polygons

Discrete Applied Mathematics
A nearly optimal algorithm for covering the interior of an Art Gallery

Pattern Recognition
Link distance and shortest path problems in the plane

Computational Geometry: Theory and Applications
Guarding polyominoes

Proceedings of the twenty-seventh annual symposium on Computational geometry
Terrain Guarding is NP-Hard

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
Exact solutions and bounds for general art gallery problems

Journal of Experimental Algorithmics (JEA)
Minimum covering with travel cost

Journal of Combinatorial Optimization
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
Efficient algorithms for pursuing moving evaders in terrains

Proceedings of the 20th International Conference on Advances in Geographic Information Systems

Quantified Score

Hi-index	0.89

Visualization

Abstract

Let P be a polygon with n vertices. We say that two points of P see each other if the line segment connecting them lies inside (the closure of) P. In this paper we present efficient approximation algorithms for finding the smallest set G of points of P so that each point of P is seen by at least one point of G, and the points of G are constrained to be belong to the set of vertices of an arbitrarily dense grind. We also present similar algorithms for terrains and polygons with holes.