Optimal grid representations
A graph G is a grid intersection graph if G is the intersection graph of ℋ ∪ ℐ, where ℋ and ℐ are, respectively, finite families of horizontal and vertical linear segments in the plane such that no two parallel segments intersect. (This definition implies that every grid intersection graph is bipart...
| Autores: | , , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2004 |
| País: | Brasil |
| Institución: | Universidade Federal do Rio de Janeiro (UFRJ) |
| Repositorio: | Repositório Institucional da UFRJ |
| Idioma: | inglés |
| OAI Identifier: | oai:pantheon.ufrj.br:11422/2582 |
| Acceso en línea: | http://hdl.handle.net/11422/2582 |
| Access Level: | acceso abierto |
| Palabra clave: | Intersection graph of segments Grid intersection graph Grid representation Integer programming CNPQ::ENGENHARIAS::ENGENHARIA ELETRICA::TELECOMUNICACOES |
| id |
BR_bce4acf902fa4bc08c30cfad5fcffe44 |
|---|---|
| oai_identifier_str |
oai:pantheon.ufrj.br:11422/2582 |
| network_acronym_str |
BR |
| network_name_str |
Brasil |
| repository_id_str |
|
| spelling |
Optimal grid representationsIntersection graph of segmentsGrid intersection graphGrid representationInteger programmingCNPQ::ENGENHARIAS::ENGENHARIA ELETRICA::TELECOMUNICACOESA graph G is a grid intersection graph if G is the intersection graph of ℋ ∪ ℐ, where ℋ and ℐ are, respectively, finite families of horizontal and vertical linear segments in the plane such that no two parallel segments intersect. (This definition implies that every grid intersection graph is bipartite.) The family ℋ ∪ ℐ is a representation of G. As a consequence of a characterization of grid intersection graphs by Kratochvíl, we observe that when a bipartite graph G = (U ∪ W, E) with minimum degree at least two is a grid intersection graph, then there exists a normalized representation of G on the (r × s)-grid for r = |U| and s = |W|, that is, a representation in which all end points of segments have integer-valued coordinates belonging to {(x, y) ∈ N × N | 1 ≤ y ≤ r, 1 ≤ x ≤ s} and the representative segment of each vertex lies on a distinct horizontal or vertical line. A natural problem, with potential applications to circuit layout, is the following: among all the possible normalized representations of G, find a representation ℛ such that the sum of the lengths of the segments in ℛ is minimum. In this work we introduce this problem and present a mixed integer programming formulation to solve it.CNPqFAPERJWiley Subscription Services, Inc., A Wiley CompanyEstados UnidosInstituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de EngenhariaInstituto Tércio Pacitti de Aplicações e Pesquisas Computacionais2017-08-04T11:07:24Z2023-12-21T03:03:45Z2004-08-09info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleFampa, M. H. C., Klein, S., Protti, F. and Rêgo, D. C. A. (2004), Optimal grid representations. Networks, 44 (3): 187–193.1097-0037http://hdl.handle.net/11422/258210.1002/net.20032engNetworksinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRJinstname:Universidade Federal do Rio de Janeiro (UFRJ)instacron:UFRJFampa, M. H. C.Klein, S.Protti, F.Rêgo, D. C. A.2023-12-21T03:03:45Zoai:pantheon.ufrj.br:11422/2582Repositório InstitucionalPUBhttp://www.pantheon.ufrj.br/oai/requestpantheon@sibi.ufrj.bropendoar:2023-12-21T03:03:45Repositório Institucional da UFRJ - Universidade Federal do Rio de Janeiro (UFRJ)false |
| dc.title.none.fl_str_mv |
Optimal grid representations |
| title |
Optimal grid representations |
| spellingShingle |
Optimal grid representations Fampa, M. H. C. Intersection graph of segments Grid intersection graph Grid representation Integer programming CNPQ::ENGENHARIAS::ENGENHARIA ELETRICA::TELECOMUNICACOES |
| title_short |
Optimal grid representations |
| title_full |
Optimal grid representations |
| title_fullStr |
Optimal grid representations |
| title_full_unstemmed |
Optimal grid representations |
| title_sort |
Optimal grid representations |
| dc.creator.none.fl_str_mv |
Fampa, M. H. C. Klein, S. Protti, F. Rêgo, D. C. A. |
| author |
Fampa, M. H. C. |
| author_facet |
Fampa, M. H. C. Klein, S. Protti, F. Rêgo, D. C. A. |
| author_role |
author |
| author2 |
Klein, S. Protti, F. Rêgo, D. C. A. |
| author2_role |
author author author |
| dc.subject.por.fl_str_mv |
Intersection graph of segments Grid intersection graph Grid representation Integer programming CNPQ::ENGENHARIAS::ENGENHARIA ELETRICA::TELECOMUNICACOES |
| topic |
Intersection graph of segments Grid intersection graph Grid representation Integer programming CNPQ::ENGENHARIAS::ENGENHARIA ELETRICA::TELECOMUNICACOES |
| description |
A graph G is a grid intersection graph if G is the intersection graph of ℋ ∪ ℐ, where ℋ and ℐ are, respectively, finite families of horizontal and vertical linear segments in the plane such that no two parallel segments intersect. (This definition implies that every grid intersection graph is bipartite.) The family ℋ ∪ ℐ is a representation of G. As a consequence of a characterization of grid intersection graphs by Kratochvíl, we observe that when a bipartite graph G = (U ∪ W, E) with minimum degree at least two is a grid intersection graph, then there exists a normalized representation of G on the (r × s)-grid for r = |U| and s = |W|, that is, a representation in which all end points of segments have integer-valued coordinates belonging to {(x, y) ∈ N × N | 1 ≤ y ≤ r, 1 ≤ x ≤ s} and the representative segment of each vertex lies on a distinct horizontal or vertical line. A natural problem, with potential applications to circuit layout, is the following: among all the possible normalized representations of G, find a representation ℛ such that the sum of the lengths of the segments in ℛ is minimum. In this work we introduce this problem and present a mixed integer programming formulation to solve it. |
| publishDate |
2004 |
| dc.date.none.fl_str_mv |
2004-08-09 2017-08-04T11:07:24Z 2023-12-21T03:03:45Z |
| dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
| dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
| format |
article |
| status_str |
publishedVersion |
| dc.identifier.uri.fl_str_mv |
Fampa, M. H. C., Klein, S., Protti, F. and Rêgo, D. C. A. (2004), Optimal grid representations. Networks, 44 (3): 187–193. 1097-0037 http://hdl.handle.net/11422/2582 10.1002/net.20032 |
| identifier_str_mv |
Fampa, M. H. C., Klein, S., Protti, F. and Rêgo, D. C. A. (2004), Optimal grid representations. Networks, 44 (3): 187–193. 1097-0037 10.1002/net.20032 |
| url |
http://hdl.handle.net/11422/2582 |
| dc.language.iso.fl_str_mv |
eng |
| language |
eng |
| dc.relation.none.fl_str_mv |
Networks |
| dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
| eu_rights_str_mv |
openAccess |
| dc.publisher.none.fl_str_mv |
Wiley Subscription Services, Inc., A Wiley Company Estados Unidos Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia Instituto Tércio Pacitti de Aplicações e Pesquisas Computacionais |
| publisher.none.fl_str_mv |
Wiley Subscription Services, Inc., A Wiley Company Estados Unidos Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia Instituto Tércio Pacitti de Aplicações e Pesquisas Computacionais |
| dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFRJ instname:Universidade Federal do Rio de Janeiro (UFRJ) instacron:UFRJ |
| instname_str |
Universidade Federal do Rio de Janeiro (UFRJ) |
| instacron_str |
UFRJ |
| institution |
UFRJ |
| reponame_str |
Repositório Institucional da UFRJ |
| collection |
Repositório Institucional da UFRJ |
| repository.name.fl_str_mv |
Repositório Institucional da UFRJ - Universidade Federal do Rio de Janeiro (UFRJ) |
| repository.mail.fl_str_mv |
pantheon@sibi.ufrj.br |
| _version_ |
1853662090496049152 |
| score |
15,301603 |