A Linear Algorithm for Resource Tripartitioning Triconnected Planar Graphs
Autor(a) principal: | |
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Data de Publicação: | 2010 |
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/301 |
Resumo: | Given a connected graph G = (V,E), a set Vr ⊆ V of r special vertices, three distinct base vertices u1, u2, u3 ∈ V and three natural numbers r1, r2, r3 such that r1 + r2 + r3 = r, we wish to find a partition V1, V2, V3 of V such that Vi contains ui and ri vertices from Vr, and Vi induces a connected subgraph of G for each i, 1 ≤ i ≤ 3. We call a vertex in Vr a resource vertex and the problem above of partitioning vertices of G as the resource 3-partitioning problem. In this paper, we give a linear-time algorithm for finding a resource tripartition of a 3-connected planar graph G. Our algortihm is based on a nonseparating ear decomposition of G and st-numbering of G. We also present a linear algorithm tofind a nonseparating ear decomposition of a 3-connected planar graph. This algorithm has bounds on ear-length and number of ears. |
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INFOCOMP: Jornal de Ciência da Computação |
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A Linear Algorithm for Resource Tripartitioning Triconnected Planar GraphsAlgorithmNonseparating ear decompositionPlanar graphResource trip artitioningResource bipartitioningst-numberingTriconnected graphGiven a connected graph G = (V,E), a set Vr ⊆ V of r special vertices, three distinct base vertices u1, u2, u3 ∈ V and three natural numbers r1, r2, r3 such that r1 + r2 + r3 = r, we wish to find a partition V1, V2, V3 of V such that Vi contains ui and ri vertices from Vr, and Vi induces a connected subgraph of G for each i, 1 ≤ i ≤ 3. We call a vertex in Vr a resource vertex and the problem above of partitioning vertices of G as the resource 3-partitioning problem. In this paper, we give a linear-time algorithm for finding a resource tripartition of a 3-connected planar graph G. Our algortihm is based on a nonseparating ear decomposition of G and st-numbering of G. We also present a linear algorithm tofind a nonseparating ear decomposition of a 3-connected planar graph. This algorithm has bounds on ear-length and number of ears.Editora da UFLA2010-06-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://infocomp.dcc.ufla.br/index.php/infocomp/article/view/301INFOCOMP Journal of Computer Science; Vol. 9 No. 2 (2010): June, 2010; 39-481982-33631807-4545reponame:INFOCOMP: Jornal de Ciência da Computaçãoinstname:Universidade Federal de Lavras (UFLA)instacron:UFLAenghttps://infocomp.dcc.ufla.br/index.php/infocomp/article/view/301/286Copyright (c) 2016 INFOCOMP Journal of Computer Scienceinfo:eu-repo/semantics/openAccessAwal, TanveerRahman, MD. Saidur2015-07-29T11:42:19Zoai:infocomp.dcc.ufla.br:article/301Revistahttps://infocomp.dcc.ufla.br/index.php/infocompPUBhttps://infocomp.dcc.ufla.br/index.php/infocomp/oaiinfocomp@dcc.ufla.br||apfreire@dcc.ufla.br1982-33631807-4545opendoar:2024-05-21T19:54:30.612882INFOCOMP: Jornal de Ciência da Computação - Universidade Federal de Lavras (UFLA)true |
dc.title.none.fl_str_mv |
A Linear Algorithm for Resource Tripartitioning Triconnected Planar Graphs |
title |
A Linear Algorithm for Resource Tripartitioning Triconnected Planar Graphs |
spellingShingle |
A Linear Algorithm for Resource Tripartitioning Triconnected Planar Graphs Awal, Tanveer Algorithm Nonseparating ear decomposition Planar graph Resource trip artitioning Resource bipartitioning st-numbering Triconnected graph |
title_short |
A Linear Algorithm for Resource Tripartitioning Triconnected Planar Graphs |
title_full |
A Linear Algorithm for Resource Tripartitioning Triconnected Planar Graphs |
title_fullStr |
A Linear Algorithm for Resource Tripartitioning Triconnected Planar Graphs |
title_full_unstemmed |
A Linear Algorithm for Resource Tripartitioning Triconnected Planar Graphs |
title_sort |
A Linear Algorithm for Resource Tripartitioning Triconnected Planar Graphs |
author |
Awal, Tanveer |
author_facet |
Awal, Tanveer Rahman, MD. Saidur |
author_role |
author |
author2 |
Rahman, MD. Saidur |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Awal, Tanveer Rahman, MD. Saidur |
dc.subject.por.fl_str_mv |
Algorithm Nonseparating ear decomposition Planar graph Resource trip artitioning Resource bipartitioning st-numbering Triconnected graph |
topic |
Algorithm Nonseparating ear decomposition Planar graph Resource trip artitioning Resource bipartitioning st-numbering Triconnected graph |
description |
Given a connected graph G = (V,E), a set Vr ⊆ V of r special vertices, three distinct base vertices u1, u2, u3 ∈ V and three natural numbers r1, r2, r3 such that r1 + r2 + r3 = r, we wish to find a partition V1, V2, V3 of V such that Vi contains ui and ri vertices from Vr, and Vi induces a connected subgraph of G for each i, 1 ≤ i ≤ 3. We call a vertex in Vr a resource vertex and the problem above of partitioning vertices of G as the resource 3-partitioning problem. In this paper, we give a linear-time algorithm for finding a resource tripartition of a 3-connected planar graph G. Our algortihm is based on a nonseparating ear decomposition of G and st-numbering of G. We also present a linear algorithm tofind a nonseparating ear decomposition of a 3-connected planar graph. This algorithm has bounds on ear-length and number of ears. |
publishDate |
2010 |
dc.date.none.fl_str_mv |
2010-06-01 |
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/301 |
url |
https://infocomp.dcc.ufla.br/index.php/infocomp/article/view/301 |
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/301/286 |
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. 9 No. 2 (2010): June, 2010; 39-48 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_ |
1799874740945420288 |