Covering orthogonal polygons with star polygons: the perfect graph approach
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Minimum K-partitioning of rectilinear polygons
Journal of Symbolic Computation
Note on covering monotone orthogonal polygons with star-shaped polygons
Information Processing Letters
On guarding the vertices of rectilinear domains
Computational Geometry: Theory and Applications
A nearly optimal sensor placement algorithm for boundary coverage
Pattern Recognition
Note: Approximation algorithms for art gallery problems in polygons
Discrete Applied Mathematics
Greedy geographic routing in large-scale sensor networks: a minimum network decomposition approach
IEEE/ACM Transactions on Networking (TON)
Fast vertex guarding for polygons with and without holes
Computational Geometry: Theory and Applications
Approximate partitioning of 2D objects into orthogonally convex components
Computer Vision and Image Understanding
Triangulating and guarding realistic polygons
Computational Geometry: Theory and Applications
| Hi-index | 754.84 |
The inherent computational complexity of polygon decomposition problems is of theoretical interest to researchers in the field of computational geometry and of practical interest to those working in syntactic pattern recognition. Three polygon decomposition problems are shown to be NP-hard and thus unlikely to admit efficient algorithms. The problems are to find minimum decompositions of a polygonal region into (perhaps overlapping) convex, star-shaped, or spiral subsets. We permit the polygonal region to contain holes. The proofs are by transformation from Boolean three-satisfiability, a known NP-complete problem. Several open problems are discussed.