Computational complexity of art gallery problems
IEEE Transactions on Information Theory
Art gallery theorems and algorithms
Art gallery theorems and algorithms
Covering orthogonal polygons with star polygons: the perfect graph approach
Journal of Computer and System Sciences
Computational Geometry: Theory and Applications
A randomized art-gallery algorithm for sensor placement
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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
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
Some NP-hard polygon decomposition problems
IEEE Transactions on Information Theory
A Scheme for Computing Minimum Covers within Simple Regions
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Note: Approximation algorithms for art gallery problems in polygons
Discrete Applied Mathematics
Algorithms and theory of computation handbook
Optimal cover of points by disks in a simple polygon
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Proceedings of the twenty-seventh annual symposium on Computational geometry
Approximation algorithms for art gallery problems in polygons and terrains
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Optimal Cover of Points by Disks in a Simple Polygon
SIAM Journal on Computing
Guarding thin orthogonal polygons is hard
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
Hi-index | 0.00 |
We prove that guarding the vertices of a rectilinear polygon P, whether by guards lying at vertices of P, or by guards lying on the boundary of P, or by guards lying anywhere in P, is NP-hard. For the first two proofs (i.e., vertex guards and boundary guards), we construct a reduction from minimum piercing of 2-intervals. The third proof is somewhat simpler; it is obtained by adapting a known reduction from minimum line cover. We also consider the problem of guarding the vertices of a 1.5D rectilinear terrain. We establish an interesting connection between this problem and the problem of computing a minimum clique cover in chordal graphs. This connection yields a 2-approximation algorithm for the guarding problem.