Reference TypeConference Proceedings
Citation KeyCoutoSouzReze:2007:ExEfAl
Author1 Couto, Marcelo C.
2 Souza, Cid C. de
3 Rezende, Pedro J. de
Affiliation1 Institute of Computing, State University of Campinas, Campinas - Brazil
2 Institute of Computing, State University of Campinas, Campinas - Brazil
3 Institute of Computing, State University of Campinas, Campinas - Brazil
TitleAn Exact and Efficient Algorithm for the Orthogonal Art Gallery Problem
Conference NameBrazilian Symposium on Computer Graphics and Image Processing, 20 (SIBGRAPI)
EditorFalcão, Alexandre Xavier
Lopes, Hélio Côrtes Vieira
Book TitleProceedings
DateOct. 7-10, 2007
Publisher CityLos Alamitos
PublisherIEEE Computer Society
Conference LocationBelo Horizonte
KeywordsArt Gallery, Exact Solution, Orthogonal Polygons, Integer Programming, Set Covering.
AbstractIn this paper, we propose an exact algorithm to solve the Orthogonal Art Gallery problem in which guards can only be placed on the vertices of the polygon $ P$ representing the gallery. Our approach is based on a discretization of $ P$ into a finite set of points in its interior. The algorithm repeatedly solves an instance of the Set Cover problem obtaining a minimum set $ Z$ of vertices of $ P$ that can view all points in the current discretization. Whenever $ P$ is completely visible from $ Z$ , the algorithm halts; otherwise, the discretization is refined and another iteration takes place. We establish that the algorithm always converges to an optimal solution by presenting a worst case analysis of the number of iterations that could be effected. Even though these could theoretically reach $ O(n^4)$ , our computational experiments reveal that, in practice, they are linear in $ n$ and, for $ nleq 200$ , they actually remain less than three in almost all instances. Furthermore, the low number of points in the initial discretization, $ O(n^2)$ , compared to the possible $ O(n^4)$ atomic visibility polygons, renders much shorter total execution times. Optimal solutions found for different classes of instances of polygons with up to 200 vertices are also described.
Tertiary TypeFull Paper
FormatPrinted, On-line.
Size210 KiB
Number of Files1
Target Filecouto-ArtGallery.pdf
Last Update2007: administrator
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