Corpus ID: 235795735

A new metaheuristic approach for the art gallery problem

@article{Bigham2021ANM,
  title={A new metaheuristic approach for the art gallery problem},
  author={Bahram Sadeghi Bigham and Sahar Badri and Nazanin Padkan},
  journal={ArXiv},
  year={2021},
  volume={abs/2107.05540}
}
In the problem “Localization and trilateration with minimum number if landmarks” we faced 3guard and classic Art Gallery Problem. The goal of the art gallery problem is to find the minimum number of guards within a simple polygon to observe and protect the entire of it. It has many applications in Robotics, Telecommunication and so on and there are some approaches to handle the art gallery problem which is theoretically NP-hard. This paper offers an efficient method based on the Particle Filter… Expand

Figures and Tables from this paper

References

SHOWING 1-10 OF 28 REFERENCES
A nearly optimal algorithm for covering the interior of an Art Gallery
TLDR
It is shown that, with some modification, the algorithm is nearly optimal also for IC, and it has been compared, for all the test polygons, with recent heuristic sensor location algorithms. Expand
The Quest for Optimal Solutions for the Art Gallery Problem: A Practical Iterative Algorithm
TLDR
This is the first time that an exact algorithm is proposed and extensively tested for this problem, and shows a remarkable performance, obtaining provably optimal solutions for every instance in a matter of minutes on a standard desktop computer. Expand
Computational complexity of art gallery problems
TLDR
The problem of determining the minimum number of vertex guards that can see an n -wall simply connected art gallery is shown to be NP-hard, and the proof can be modified to show that the problems ofetermining theminimum number of edge guards and theMinimum number of point guards in a simply connected polygonal region are also NP- hard. Expand
The art gallery problem is ∃ ℝ-complete
TLDR
It is shown that for every compact semi-algebraic set S⊂ [0,1]2 there exists a polygon with rational coordinates that enforces one of the guards to be at any position p∈ S, in any optimal guarding, which rules out many natural geometric approaches to the art gallery problem. Expand
Optimizing the Minimum Vertex Guard Set on Simple Polygons via a Genetic Algorithm
The problem of minimizing the number of vertex-guards necessary to cover a given simple polygon (MINIMUM VERTEX GUARD (MVG) problem) is NP-hard. This computational complexity opens two lines ofExpand
Locating Guards for Visibility Coverage of Polygons
TLDR
Experimental evidence is given that the heuristics proposed give a provably optimal result, while in other cases there is only a small gap between the computed upper and lower bounds on the optimal guard number. Expand
Traditional Galleries Require Fewer Watchmen
Chvatal’s watchman theorem shows if the walls of an art gallery form an n-sided polygon then at most $[ n /3 ]$ watchmen are needed to guard it, and that this number is best possible. In this paperExpand
Gsr: Geometrical Scan Registration Algorithm for Robust and Fast Robot Pose Estimation
TLDR
An attempt has been made to develop an algorithm equipped with geometric pattern registration techniques to perform exact, robust, and fast robot localization purely based on laser range data that is superior to the other localization methods based on scan matching in accuracy, processing speed, and robustness to large positioning errors. Expand
The Orthogonal Art Gallery Theorem with Constrained Guards
TLDR
It is proved that P has a guard set of cardinality at most ⌊ ( n + 3 | V ⁎ | + 2 | E ⁍ | ) / 4 ⌋ that includes each vertex in V⁎ and at least one point of each edge in E⌋. Expand
On guarding the vertices of rectilinear domains
TLDR
It is proved that guarding the vertices of a rectilinear polygon P, whether by guards lying at vertices on the boundary of P, or byguards lying anywhere in P, is NP-hard. Expand
...
1
2
3
...