On the Hyperbox – Hyperplane Intersection Problem
Autor(a) principal: | |
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Data de Publicação: | 2009 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | INFOCOMP: Jornal de Ciência da Computação |
Texto Completo: | https://infocomp.dcc.ufla.br/index.php/infocomp/article/view/278 |
Resumo: | Finding the intersection between a hyperbox and a hyperplane can be computationally expensive specially for high dimensional problems. Naive algorithms have an exponential complexity. A border node is a node (in the graph induced by the hyperbox) at or next to the intersection of the hyperbox and the hyperplane. The algorithm proposed in this paper implements a systematic way to efficiently generate border nodes; given a border node, a subset of its incident edges is explored to determine one or more intersections. This systematic exploration allows us to focus on the border region, discarding the two regions before and after the plane. Pruning those regions produces a computational cost linear on the number of vertices of the hyperpolygon that represents the intersection. |
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On the Hyperbox – Hyperplane Intersection Problemhyperboxhyperrectanglehyperplanevectorgraph searchingFinding the intersection between a hyperbox and a hyperplane can be computationally expensive specially for high dimensional problems. Naive algorithms have an exponential complexity. A border node is a node (in the graph induced by the hyperbox) at or next to the intersection of the hyperbox and the hyperplane. The algorithm proposed in this paper implements a systematic way to efficiently generate border nodes; given a border node, a subset of its incident edges is explored to determine one or more intersections. This systematic exploration allows us to focus on the border region, discarding the two regions before and after the plane. Pruning those regions produces a computational cost linear on the number of vertices of the hyperpolygon that represents the intersection.Editora da UFLA2009-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://infocomp.dcc.ufla.br/index.php/infocomp/article/view/278INFOCOMP Journal of Computer Science; Vol. 8 No. 4 (2009): December, 2009; 21-271982-33631807-4545reponame:INFOCOMP: Jornal de Ciência da Computaçãoinstname:Universidade Federal de Lavras (UFLA)instacron:UFLAenghttps://infocomp.dcc.ufla.br/index.php/infocomp/article/view/278/263Copyright (c) 2016 INFOCOMP Journal of Computer Scienceinfo:eu-repo/semantics/openAccessLara, CarlosFlores, Juan J.Calderon, Felix2015-07-22T18:26:29Zoai:infocomp.dcc.ufla.br:article/278Revistahttps://infocomp.dcc.ufla.br/index.php/infocompPUBhttps://infocomp.dcc.ufla.br/index.php/infocomp/oaiinfocomp@dcc.ufla.br||apfreire@dcc.ufla.br1982-33631807-4545opendoar:2024-05-21T19:54:29.300732INFOCOMP: Jornal de Ciência da Computação - Universidade Federal de Lavras (UFLA)true |
dc.title.none.fl_str_mv |
On the Hyperbox – Hyperplane Intersection Problem |
title |
On the Hyperbox – Hyperplane Intersection Problem |
spellingShingle |
On the Hyperbox – Hyperplane Intersection Problem Lara, Carlos hyperbox hyperrectangle hyperplane vector graph searching |
title_short |
On the Hyperbox – Hyperplane Intersection Problem |
title_full |
On the Hyperbox – Hyperplane Intersection Problem |
title_fullStr |
On the Hyperbox – Hyperplane Intersection Problem |
title_full_unstemmed |
On the Hyperbox – Hyperplane Intersection Problem |
title_sort |
On the Hyperbox – Hyperplane Intersection Problem |
author |
Lara, Carlos |
author_facet |
Lara, Carlos Flores, Juan J. Calderon, Felix |
author_role |
author |
author2 |
Flores, Juan J. Calderon, Felix |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Lara, Carlos Flores, Juan J. Calderon, Felix |
dc.subject.por.fl_str_mv |
hyperbox hyperrectangle hyperplane vector graph searching |
topic |
hyperbox hyperrectangle hyperplane vector graph searching |
description |
Finding the intersection between a hyperbox and a hyperplane can be computationally expensive specially for high dimensional problems. Naive algorithms have an exponential complexity. A border node is a node (in the graph induced by the hyperbox) at or next to the intersection of the hyperbox and the hyperplane. The algorithm proposed in this paper implements a systematic way to efficiently generate border nodes; given a border node, a subset of its incident edges is explored to determine one or more intersections. This systematic exploration allows us to focus on the border region, discarding the two regions before and after the plane. Pruning those regions produces a computational cost linear on the number of vertices of the hyperpolygon that represents the intersection. |
publishDate |
2009 |
dc.date.none.fl_str_mv |
2009-12-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://infocomp.dcc.ufla.br/index.php/infocomp/article/view/278 |
url |
https://infocomp.dcc.ufla.br/index.php/infocomp/article/view/278 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://infocomp.dcc.ufla.br/index.php/infocomp/article/view/278/263 |
dc.rights.driver.fl_str_mv |
Copyright (c) 2016 INFOCOMP Journal of Computer Science info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2016 INFOCOMP Journal of Computer Science |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Editora da UFLA |
publisher.none.fl_str_mv |
Editora da UFLA |
dc.source.none.fl_str_mv |
INFOCOMP Journal of Computer Science; Vol. 8 No. 4 (2009): December, 2009; 21-27 1982-3363 1807-4545 reponame:INFOCOMP: Jornal de Ciência da Computação instname:Universidade Federal de Lavras (UFLA) instacron:UFLA |
instname_str |
Universidade Federal de Lavras (UFLA) |
instacron_str |
UFLA |
institution |
UFLA |
reponame_str |
INFOCOMP: Jornal de Ciência da Computação |
collection |
INFOCOMP: Jornal de Ciência da Computação |
repository.name.fl_str_mv |
INFOCOMP: Jornal de Ciência da Computação - Universidade Federal de Lavras (UFLA) |
repository.mail.fl_str_mv |
infocomp@dcc.ufla.br||apfreire@dcc.ufla.br |
_version_ |
1799874740908720128 |