Approximate guarding of monotone and rectilinear polygons

Authors:
Bengt J. Nilsson
Affiliations:
Technology and Society, Malmö University College, Malmö, Sweden
Venue:
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Year:
2005

Citing 14
Cited 12

Computational complexity of art gallery problems

IEEE Transactions on Information Theory
Corrections to Lee's visibility polygon algorithm

BIT
Heuristics for minimum decompositions of polygons

Heuristics for minimum decompositions of polygons
Art gallery theorems and algorithms

Art gallery theorems and algorithms
Optimum watchman routes

Information Processing Letters
On rectilinear link distance

Computational Geometry: Theory and Applications
The Art Gallery theorem for polygons with holes

SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Inapproximability Results for Guarding Polygons without Holes

ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
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
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 terrain guarding

SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Covering polygons is hard

SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Triangulating a simple polygon in linear time

SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science

Finding minimum hidden guard sets in polygons: tight approximability results

Computational Geometry: Theory and Applications
Maximizing the guarded boundary of an Art Gallery is APX-complete

Computational Geometry: Theory and Applications
On guarding the vertices of rectilinear domains

Computational Geometry: Theory and Applications
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
Note: Approximation algorithms for art gallery problems in polygons

Discrete Applied Mathematics
Terrain guarding is NP-hard

SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Guarding polyominoes

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

SIAM Journal on Computing
On guarding rectilinear domains

SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Approximation algorithms for art gallery problems in polygons and terrains

WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Guarding thin orthogonal polygons is hard

FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

We show a constant factor approximation algorithm for interior guarding of monotone polygons. Using this algorithm we obtain an approximation algorithm for interior guarding rectilinear polygons that has an approximation factor independent of the number of vertices of the polygon. If the size of the smallest interior guard cover is OPT for a rectilinear polygon, our algorithm produces a guard set of size O(OPT2).