Locating Guards for Visibility Coverage of Polygons

Amit, Yoav; Mitchell, Joseph S. B.; Packer, Eli

doi:10.1137/1.9781611972870.12

Cited by 20 publications

(14 citation statements)

References 30 publications

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“…Previous work mostly consists of heuristics [Amit et al 2007] with good practical performance. To the best of our knowledge, there is little work on good lower bounds.…”

Section: Related Workmentioning

confidence: 99%

“…To the best of our knowledge, there is little work on good lower bounds. Amit et al [2007] are the only ones to consider a lower bound for the general AGP, with the entire polygon to cover. They use the lower bound to compare heuristic solutions, with the guards taken from different candidate sets, such as vertices and more enhanced points.…”

Section: Related Workmentioning

confidence: 99%

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Exact solutions and bounds for general art gallery problems

Kröller

Baumgärtner

Fekete

et al. 2012

ACM J. Exp. Algorithmics

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The classical Art Gallery Problem asks for the minimum number of guards that achieve visibility coverage of a given polygon. This problem is known to be NP-hard, even for very restricted and discrete special cases. For the case of vertex guards and simple orthogonal polygons, Cuoto et al. have recently developed an exact method that is based on a set-cover approach. For the general problem (in which both the set of possible guard positions and the point set to be guarded are uncountable), neither constant-factor approximation algorithms nor exact solution methods are known.We present a primal-dual algorithm based on linear programming that provides lower bounds on the necessary number of guards in every step and-in case of convergence and integrality-ends with an optimal solution. We describe our implementation and give experimental results for an assortment of polygons, including nonorthogonal polygons with holes.

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“…Previous work mostly consists of heuristics [Amit et al 2007] with good practical performance. To the best of our knowledge, there is little work on good lower bounds.…”

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Exact solutions and bounds for general art gallery problems

Kröller

Baumgärtner

Fekete

et al. 2012

ACM J. Exp. Algorithmics

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“…Since the corresponding minimization problem has been proven NPhard [9] even for orthogonal polygons [10], placement of suboptimal numbers of guards has been studied [2], as well as a few approximation algorithms [1].…”

Section: Introductionmentioning

confidence: 99%

An IP solution to the art gallery problem

Couto

Rezende

Souza

2009

Proceedings of the Twenty-Fifth Annual Symposium on Computational Geometry

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The Art Gallery problem (agp) consists of minimizing the number of guards required to cover a gallery whose boundary is a simple polygon P . In this paper, we describe an Integer Programming based solution to agp that is presented in the accompanying video. Said solution is comprised of an exact algorithm that models discretizations of P as instances of the Set Cover problem and iteratively solves them using an IP solver. We have shown elsewhere [4] that this process always converges. A testing environment, shown in the video, has been implemented with which we have collected substantial experimental evidence that this approach is very efficient in practice, by solving instances of up to 2500 vertices.

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“…There are several works where approximation algorithms were developed to solve the MSG problem [3,9] and to compute multiple watchmen routes, a variant of the MSG problem [15]. In a recent work, metaheuristics techniques have proven to behave very well when solving the MSG problem [1].…”

Section: Introduction Related Work and Problem Definitionmentioning

confidence: 99%

Metaheuristic Approaches for the Minimum Vertex Guard Problem

Bajuelos

Martins

Canales

et al. 2009

2009 Third International Conference on Advanced Engineering Computing and Applications in Sciences

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We address the problem of stationing guards in vertices of a simple polygon in such a way that the whole polygon is guarded and the number of guards is minimum. This problem is NP-hard with relevant practical applications. In this paper we propose three metaheuristic approaches to this problem. Combined with the genetic algorithms strategy, which was proposed in [4], these four approximation algorithms have been implemented and compared. The experimental evaluation from the hybrid strategy shows significant improvement in the number of guards compared to theoretical bounds.

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Locating Guards for Visibility Coverage of Polygons

Cited by 20 publications

References 30 publications

Exact solutions and bounds for general art gallery problems

Exact solutions and bounds for general art gallery problems

An IP solution to the art gallery problem

Metaheuristic Approaches for the Minimum Vertex Guard Problem

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