Lagrangean relaxation bounds for point-feature cartographic label placement problem
Autor(a) principal: | |
---|---|
Data de Publicação: | 2006 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Pesquisa operacional (Online) |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382006000300002 |
Resumo: | The objective of the point-feature cartographic label placement problem (PFCLP) is to give more legibility to an automatic map creation, placing point labels in clear positions. Many researchers consider distinct approaches for PFCLP, such as to obtain the maximum number of labeled points that can be placed without overlapping or to obtain the maximum number of labeled points without overlaps considering that all points must be labeled. This paper considers another variant of the problem in which one has to minimize the number of overlaps while all points are labeled in the map. A conflict graph is initially defined and a mathematical formulation of binary integer linear programming is presented. Commercial optimization packages could not solve large instances exactly using this formulation over instances proposed in the literature. A heuristic is then examined considering a Lagrangean relaxation performed after an initial partition of the conflict graph into clusters. This decomposition allowed us to introduce tight lower and upper bounds for PFCLP. |
id |
SOBRAPO-1_89249c8019ae5d72b47b71ed73c06dce |
---|---|
oai_identifier_str |
oai:scielo:S0101-74382006000300002 |
network_acronym_str |
SOBRAPO-1 |
network_name_str |
Pesquisa operacional (Online) |
repository_id_str |
|
spelling |
Lagrangean relaxation bounds for point-feature cartographic label placement problemlabel placementmodelingLagrangean relaxationThe objective of the point-feature cartographic label placement problem (PFCLP) is to give more legibility to an automatic map creation, placing point labels in clear positions. Many researchers consider distinct approaches for PFCLP, such as to obtain the maximum number of labeled points that can be placed without overlapping or to obtain the maximum number of labeled points without overlaps considering that all points must be labeled. This paper considers another variant of the problem in which one has to minimize the number of overlaps while all points are labeled in the map. A conflict graph is initially defined and a mathematical formulation of binary integer linear programming is presented. Commercial optimization packages could not solve large instances exactly using this formulation over instances proposed in the literature. A heuristic is then examined considering a Lagrangean relaxation performed after an initial partition of the conflict graph into clusters. This decomposition allowed us to introduce tight lower and upper bounds for PFCLP.Sociedade Brasileira de Pesquisa Operacional2006-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382006000300002Pesquisa Operacional v.26 n.3 2006reponame:Pesquisa operacional (Online)instname:Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)instacron:SOBRAPO10.1590/S0101-74382006000300002info:eu-repo/semantics/openAccessRibeiro,Glaydston MattosLorena,Luiz Antonio Nogueiraeng2007-02-23T00:00:00Zoai:scielo:S0101-74382006000300002Revistahttp://www.scielo.br/popehttps://old.scielo.br/oai/scielo-oai.php||sobrapo@sobrapo.org.br1678-51420101-7438opendoar:2007-02-23T00:00Pesquisa operacional (Online) - Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)false |
dc.title.none.fl_str_mv |
Lagrangean relaxation bounds for point-feature cartographic label placement problem |
title |
Lagrangean relaxation bounds for point-feature cartographic label placement problem |
spellingShingle |
Lagrangean relaxation bounds for point-feature cartographic label placement problem Ribeiro,Glaydston Mattos label placement modeling Lagrangean relaxation |
title_short |
Lagrangean relaxation bounds for point-feature cartographic label placement problem |
title_full |
Lagrangean relaxation bounds for point-feature cartographic label placement problem |
title_fullStr |
Lagrangean relaxation bounds for point-feature cartographic label placement problem |
title_full_unstemmed |
Lagrangean relaxation bounds for point-feature cartographic label placement problem |
title_sort |
Lagrangean relaxation bounds for point-feature cartographic label placement problem |
author |
Ribeiro,Glaydston Mattos |
author_facet |
Ribeiro,Glaydston Mattos Lorena,Luiz Antonio Nogueira |
author_role |
author |
author2 |
Lorena,Luiz Antonio Nogueira |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Ribeiro,Glaydston Mattos Lorena,Luiz Antonio Nogueira |
dc.subject.por.fl_str_mv |
label placement modeling Lagrangean relaxation |
topic |
label placement modeling Lagrangean relaxation |
description |
The objective of the point-feature cartographic label placement problem (PFCLP) is to give more legibility to an automatic map creation, placing point labels in clear positions. Many researchers consider distinct approaches for PFCLP, such as to obtain the maximum number of labeled points that can be placed without overlapping or to obtain the maximum number of labeled points without overlaps considering that all points must be labeled. This paper considers another variant of the problem in which one has to minimize the number of overlaps while all points are labeled in the map. A conflict graph is initially defined and a mathematical formulation of binary integer linear programming is presented. Commercial optimization packages could not solve large instances exactly using this formulation over instances proposed in the literature. A heuristic is then examined considering a Lagrangean relaxation performed after an initial partition of the conflict graph into clusters. This decomposition allowed us to introduce tight lower and upper bounds for PFCLP. |
publishDate |
2006 |
dc.date.none.fl_str_mv |
2006-12-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382006000300002 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382006000300002 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S0101-74382006000300002 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
text/html |
dc.publisher.none.fl_str_mv |
Sociedade Brasileira de Pesquisa Operacional |
publisher.none.fl_str_mv |
Sociedade Brasileira de Pesquisa Operacional |
dc.source.none.fl_str_mv |
Pesquisa Operacional v.26 n.3 2006 reponame:Pesquisa operacional (Online) instname:Sociedade Brasileira de Pesquisa Operacional (SOBRAPO) instacron:SOBRAPO |
instname_str |
Sociedade Brasileira de Pesquisa Operacional (SOBRAPO) |
instacron_str |
SOBRAPO |
institution |
SOBRAPO |
reponame_str |
Pesquisa operacional (Online) |
collection |
Pesquisa operacional (Online) |
repository.name.fl_str_mv |
Pesquisa operacional (Online) - Sociedade Brasileira de Pesquisa Operacional (SOBRAPO) |
repository.mail.fl_str_mv |
||sobrapo@sobrapo.org.br |
_version_ |
1750318016614105088 |