Reference Type | `Conference Proceedings` |

Repository | `sid.inpe.br/sibgrapi@80/2007/07.09.17.59` |

Metadata | `sid.inpe.br/sibgrapi@80/2007/07.09.17.59.10` |

Site | `sibgrapi.sid.inpe.br` |

Citation Key | `CoutoSouzReze:2007:ExEfAl` |

Author | `1 Couto, Marcelo C.` 2 Souza, Cid C. de 3 Rezende, Pedro J. de |

Affiliation | `1 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 |

Title | `An Exact and Efficient Algorithm for the Orthogonal Art Gallery Problem ` |

Conference Name | `Brazilian Symposium on Computer Graphics and Image Processing, 20 (SIBGRAPI)` |

Year | **2007** |

Editor | `Falcão, Alexandre Xavier` Lopes, Hélio Côrtes Vieira |

Book Title | `Proceedings` |

Date | `Oct. 7-10, 2007` |

Publisher City | `Los Alamitos` |

Publisher | `IEEE Computer Society` |

Conference Location | `Belo Horizonte` |

Keywords | `Art Gallery, Exact Solution, Orthogonal Polygons, Integer Programming, Set Covering.` |

Abstract | `In 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.` |

Language | `en` |

Tertiary Type | `Full Paper` |

Format | `Printed, On-line.` |

Size | `210 KiB` |

Number of Files | `1` |

Target File | `couto-ArtGallery.pdf` |

Last Update | `2007:07.09.17.59.09 sid.inpe.br/banon/2001/03.30.15.38 administrator` |

Metadata Last Update | `2020:02.19.03.06.18 sid.inpe.br/banon/2001/03.30.15.38 administrator {D 2007}` |

Document Stage | `completed` |

Is the master or a copy? | `is the master` |

Mirror | `dpi.inpe.br/banon-pc2@80/2006/08.30.19.27` |

User Group | `cid@ic.unicamp.br administrator` |

Visibility | `shown` |

Transferable | `1` |

Host Collection | `sid.inpe.br/banon/2001/03.30.15.38` |

Content Type | `External Contribution` |

source Directory Content | `there are no files` |

agreement Directory Content | `there are no files` |

History | `2007-07-09 17:59:10 :: cid@ic.unicamp.br -> administrator :: ` 2007-08-02 21:17:16 :: administrator -> cid@ic.unicamp.br :: 2008-07-17 14:09:42 :: cid@ic.unicamp.br -> administrator :: 2009-08-13 20:38:18 :: administrator -> banon :: 2010-08-28 20:02:26 :: banon -> administrator :: 2020-02-19 03:06:18 :: administrator -> :: 2007 |

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Access Date | `2020, Oct. 26` |