Art gallery theorems and algorithms
Art gallery theorems and algorithms
An Optimal Algorithm for Detecting Weak Visibility of a Polygon
IEEE Transactions on Computers
Planning for complete sensor coverage in inspection
Computer Vision and Image Understanding
A survey of automated visual inspection
Computer Vision and Image Understanding
A randomized art-gallery algorithm for sensor placement
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
View planning for automated three-dimensional object reconstruction and inspection
ACM Computing Surveys (CSUR)
A fast algorithm for the maximum clique problem
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
Guarding galleries and terrains
Information Processing Letters
An Optimal Algorithm for Determining the Visibility of a Polygon from an Edge
IEEE Transactions on Computers
A nearly optimal sensor placement algorithm for boundary coverage
Pattern Recognition
An algorithm for finding a maximum clique in a graph
Operations Research Letters
An exact algorithm for the maximum clique problem
Operations Research Letters
Active vision in robotic systems: A survey of recent developments
International Journal of Robotics Research
Hi-index | 0.10 |
Locating sensors in 2D can be modelled as an Art Gallery problem. Tasks such as surveillance require observing or ''covering'' the interior of a polygon with a minimum number of sensors (IC, Interior Covering). Edge Covering (EC) is sufficient for tasks such as inspection or image based rendering. As IC, also EC is NP-hard, and no finite algorithm is known for its exact solution. A number of heuristics have been proposed for EC, but their performances with respect to optimality are unknown. Recently, a lower bound for the cardinality of the optimal EC solution, specific of a given polygon, has been proposed. It allows assessing the performances of approximate EC sensor location algorithms. In this paper, we propose a new lower bound. It is always greater than, or equal to the previous, and can be computed in reasonable time for environments with up to a few hundreds of edges. Tests over hundreds of polygons using a recent incremental EC algorithm show that the gap between the cardinality of the solution provided by the algorithm and the new lower bound is substantially reduced, and then the new lower bound outperforms the previous one.