Problema de particionamento em subgrafos complementares: complexidade e convexidade
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFG |
dARK ID: | ark:/38995/00130000064k7 |
Texto Completo: | http://repositorio.bc.ufg.br/tede/handle/tede/10180 |
Resumo: | In this work, we introduce the PARTITION INTO COMPLEMENTARY SUBGRAPHS (COMP-SUB(Pi)) problem, which receives as input a graph H and an edge set property Pi, and the goal is determining whether is possible to decompose the graph H into complementary subgraphs G and \bar{G} such that the edge set M between G and \bar{G} satisfies property Pi. COMP-SUB(Pi) generalizes the recognition of complementary prisms problem, which is the case when Pi is a perfect matching between corresponding vertices of G and \bar{G}. When Pi is arbitrary, we show results for k-clique or k-independent set free graphs. On property P_\emptyset which considers M =\emptyset, we show that COMP-SUB(P_\emptyset) is GI-complete for chordal graphs, but can be solved efficiently for permutation, comparability, co- comparability and co-interval graphs. Furthermore, we obtain characterizations for some subclasses of chordal graphs. We also obtain results for Pi_{Kn,n} , the case when M has all the possible edges between G and \bar{G} and for Pi_{PERF}, the case which considers M as a perfect matching. In particular, we show that COMP-SUB(Pi_{PERF}) problem is GI-hard, and we obtain characterizations for this problem when the input graph H is a cograph, a chordal or a distance-hereditary graph. On the other hand, we address three parameters of the geodetic convexity for complementary prisms: the hull number, the geodetic number and the convexity number. We obtain results on the hull number for complementary prisms G\bar{G} when both G e \bar{G} are connected. On the second and third parameter, we show that the decision problems related to the geodetic number and convexity number are NP-complete even restricted to complementary prisms. We also establish lower bounds on the geodetic number for G\bar{G} when G or \bar{G} have simplicial vertices and we determine the convexity number for G\bar{G} when G is disconnected, or G is a cograph. |
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Castonguay, Dianehttp://lattes.cnpq.br/4005898623592261Coelho, Erika Morais Martinshttp://lattes.cnpq.br/9389487015938509Castonguay, DianeCoelho, Erika Morais MartinsProtti, FábioSzwarcfiter, Jayme LuizPinto, Leizer de Limahttp://lattes.cnpq.br/8971175373328824Nascimento, Julliano Rosa2019-11-18T12:32:30Z2019-11-11NASCIMENTO, J. R. Problema de particionamento em subgrafos complementares: complexidade e convexidade. 2019. 129 f. Tese (Doutorado em Ciência da Computação) - Universidade Federal de Goiás, Foiânia, 2019.http://repositorio.bc.ufg.br/tede/handle/tede/10180ark:/38995/00130000064k7In this work, we introduce the PARTITION INTO COMPLEMENTARY SUBGRAPHS (COMP-SUB(Pi)) problem, which receives as input a graph H and an edge set property Pi, and the goal is determining whether is possible to decompose the graph H into complementary subgraphs G and \bar{G} such that the edge set M between G and \bar{G} satisfies property Pi. COMP-SUB(Pi) generalizes the recognition of complementary prisms problem, which is the case when Pi is a perfect matching between corresponding vertices of G and \bar{G}. When Pi is arbitrary, we show results for k-clique or k-independent set free graphs. On property P_\emptyset which considers M =\emptyset, we show that COMP-SUB(P_\emptyset) is GI-complete for chordal graphs, but can be solved efficiently for permutation, comparability, co- comparability and co-interval graphs. Furthermore, we obtain characterizations for some subclasses of chordal graphs. We also obtain results for Pi_{Kn,n} , the case when M has all the possible edges between G and \bar{G} and for Pi_{PERF}, the case which considers M as a perfect matching. In particular, we show that COMP-SUB(Pi_{PERF}) problem is GI-hard, and we obtain characterizations for this problem when the input graph H is a cograph, a chordal or a distance-hereditary graph. On the other hand, we address three parameters of the geodetic convexity for complementary prisms: the hull number, the geodetic number and the convexity number. We obtain results on the hull number for complementary prisms G\bar{G} when both G e \bar{G} are connected. On the second and third parameter, we show that the decision problems related to the geodetic number and convexity number are NP-complete even restricted to complementary prisms. We also establish lower bounds on the geodetic number for G\bar{G} when G or \bar{G} have simplicial vertices and we determine the convexity number for G\bar{G} when G is disconnected, or G is a cograph.Nesta tese, introduzimos o problema PARTIÇÃO EM SUBGRAFOS COMPLEMENTARES (COMP- SUB(Pi)), que recebe como entrada um grafo H e uma propriedade de arestas Pi, e o objetivo é determinar se existe uma decomposição do grafo H em subgrafos complementares G e \bar{G} tal que o conjunto de arestas M entre G e \bar{G} satisfaça a propriedade Pi. COMP-SUB(Pi) generaliza o problema de reconhecimento dos prismas complementares, que é o caso quando Pi é um emparelhamento perfeito entre vértices correspondentes de G e \bar{G}. Para Pi uma propriedade arbitrária, mostramos resultados para grafos livres de k-clique ou k-conjunto independente. Sobre a propriedade Pi_\emptyset que considera M = \emptyset, mostramos que COMP-SUB(Pi_\emptyset) é GI-completo para grafos cordais, mas pode ser resolvido eficientemente para grafos de permutação, comparabilidade, co-comparabilidade e co-intervalo. Além disso, obtemos caracterizações para algumas subclasses de grafos cordais. Também obtemos resultados considerando Pi_{Kn,n} , o caso em que M possui todas as arestas possíveis entre G e \bar{G} e para Pi_{PERF}, o caso que considera M como um emparelhamento perfeito. Em particular, mostramos que o problema COMP-SUB(Pi_{PERF}) é GI-difícil e obtemos caracterizações para este problema quando o grafo H de entrada é um cografo, grafo cordal ou distância-hereditária. Por outro lado, também abordamos nesta tese três parâmetros da convexidade geodética para prismas complementares: o número envoltório, o número geodético e o número de convexidade. Obtemos resultados sobre o número envoltório para prismas complementares G\bar{G} quando ambos G e \bar{G} são conexos. Sobre o segundo e o terceiro parâmetro, mostramos que seus problemas de decisão são NP-completos mesmo restritos aos prismas complementares. Além disso, estabelecemos limites inferiores do número geodético de G\bar{G} quando G ou \bar{G} possuem vértices simpliciais e determinamos o número de convexidade de G\bar{G} quando G é desconexo ou G é um cografo.Submitted by Franciele Moreira (francielemoreyra@gmail.com) on 2019-11-14T15:36:47Z No. of bitstreams: 2 Tese - Julliano Rosa Nascimento - 2019.pdf: 1734348 bytes, checksum: 97feaaf3fc2f24ae8f21d4c930ebd422 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2019-11-18T12:32:30Z (GMT) No. of bitstreams: 2 Tese - Julliano Rosa Nascimento - 2019.pdf: 1734348 bytes, checksum: 97feaaf3fc2f24ae8f21d4c930ebd422 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Made available in DSpace on 2019-11-18T12:32:30Z (GMT). No. of bitstreams: 2 Tese - Julliano Rosa Nascimento - 2019.pdf: 1734348 bytes, checksum: 97feaaf3fc2f24ae8f21d4c930ebd422 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2019-11-11Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESapplication/pdfporUniversidade Federal de GoiásPrograma de Pós-graduação em Ciência da Computação (INF)UFGBrasilInstituto de Informática - INF (RG)http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessParticionamento de grafosSubgrafos complementaresIsomorfismo de grafosConvexidade geodéticaPrismas complementaresGraph partitioningComplementary subgraphsGraph isomorphismGeodetic convexityComplementary prismsCIENCIAS SOCIAIS APLICADAS::CIENCIA DA INFORMACAOProblema de particionamento em subgrafos complementares: complexidade e convexidadePartitioning a graph into complementary subgraphs: complexity and convexityinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesis-3303550325223384799600600600600-7712266734633644768-88210291136171318082075167498588264571reponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGLICENSElicense.txtlicense.txttext/plain; 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dc.title.eng.fl_str_mv |
Problema de particionamento em subgrafos complementares: complexidade e convexidade |
dc.title.alternative.eng.fl_str_mv |
Partitioning a graph into complementary subgraphs: complexity and convexity |
title |
Problema de particionamento em subgrafos complementares: complexidade e convexidade |
spellingShingle |
Problema de particionamento em subgrafos complementares: complexidade e convexidade Nascimento, Julliano Rosa Particionamento de grafos Subgrafos complementares Isomorfismo de grafos Convexidade geodética Prismas complementares Graph partitioning Complementary subgraphs Graph isomorphism Geodetic convexity Complementary prisms CIENCIAS SOCIAIS APLICADAS::CIENCIA DA INFORMACAO |
title_short |
Problema de particionamento em subgrafos complementares: complexidade e convexidade |
title_full |
Problema de particionamento em subgrafos complementares: complexidade e convexidade |
title_fullStr |
Problema de particionamento em subgrafos complementares: complexidade e convexidade |
title_full_unstemmed |
Problema de particionamento em subgrafos complementares: complexidade e convexidade |
title_sort |
Problema de particionamento em subgrafos complementares: complexidade e convexidade |
author |
Nascimento, Julliano Rosa |
author_facet |
Nascimento, Julliano Rosa |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Castonguay, Diane |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/4005898623592261 |
dc.contributor.advisor-co1.fl_str_mv |
Coelho, Erika Morais Martins |
dc.contributor.advisor-co1Lattes.fl_str_mv |
http://lattes.cnpq.br/9389487015938509 |
dc.contributor.referee1.fl_str_mv |
Castonguay, Diane |
dc.contributor.referee2.fl_str_mv |
Coelho, Erika Morais Martins |
dc.contributor.referee3.fl_str_mv |
Protti, Fábio |
dc.contributor.referee4.fl_str_mv |
Szwarcfiter, Jayme Luiz |
dc.contributor.referee5.fl_str_mv |
Pinto, Leizer de Lima |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/8971175373328824 |
dc.contributor.author.fl_str_mv |
Nascimento, Julliano Rosa |
contributor_str_mv |
Castonguay, Diane Coelho, Erika Morais Martins Castonguay, Diane Coelho, Erika Morais Martins Protti, Fábio Szwarcfiter, Jayme Luiz Pinto, Leizer de Lima |
dc.subject.por.fl_str_mv |
Particionamento de grafos Subgrafos complementares Isomorfismo de grafos Convexidade geodética Prismas complementares |
topic |
Particionamento de grafos Subgrafos complementares Isomorfismo de grafos Convexidade geodética Prismas complementares Graph partitioning Complementary subgraphs Graph isomorphism Geodetic convexity Complementary prisms CIENCIAS SOCIAIS APLICADAS::CIENCIA DA INFORMACAO |
dc.subject.eng.fl_str_mv |
Graph partitioning Complementary subgraphs Graph isomorphism Geodetic convexity Complementary prisms |
dc.subject.cnpq.fl_str_mv |
CIENCIAS SOCIAIS APLICADAS::CIENCIA DA INFORMACAO |
description |
In this work, we introduce the PARTITION INTO COMPLEMENTARY SUBGRAPHS (COMP-SUB(Pi)) problem, which receives as input a graph H and an edge set property Pi, and the goal is determining whether is possible to decompose the graph H into complementary subgraphs G and \bar{G} such that the edge set M between G and \bar{G} satisfies property Pi. COMP-SUB(Pi) generalizes the recognition of complementary prisms problem, which is the case when Pi is a perfect matching between corresponding vertices of G and \bar{G}. When Pi is arbitrary, we show results for k-clique or k-independent set free graphs. On property P_\emptyset which considers M =\emptyset, we show that COMP-SUB(P_\emptyset) is GI-complete for chordal graphs, but can be solved efficiently for permutation, comparability, co- comparability and co-interval graphs. Furthermore, we obtain characterizations for some subclasses of chordal graphs. We also obtain results for Pi_{Kn,n} , the case when M has all the possible edges between G and \bar{G} and for Pi_{PERF}, the case which considers M as a perfect matching. In particular, we show that COMP-SUB(Pi_{PERF}) problem is GI-hard, and we obtain characterizations for this problem when the input graph H is a cograph, a chordal or a distance-hereditary graph. On the other hand, we address three parameters of the geodetic convexity for complementary prisms: the hull number, the geodetic number and the convexity number. We obtain results on the hull number for complementary prisms G\bar{G} when both G e \bar{G} are connected. On the second and third parameter, we show that the decision problems related to the geodetic number and convexity number are NP-complete even restricted to complementary prisms. We also establish lower bounds on the geodetic number for G\bar{G} when G or \bar{G} have simplicial vertices and we determine the convexity number for G\bar{G} when G is disconnected, or G is a cograph. |
publishDate |
2019 |
dc.date.accessioned.fl_str_mv |
2019-11-18T12:32:30Z |
dc.date.issued.fl_str_mv |
2019-11-11 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
NASCIMENTO, J. R. Problema de particionamento em subgrafos complementares: complexidade e convexidade. 2019. 129 f. Tese (Doutorado em Ciência da Computação) - Universidade Federal de Goiás, Foiânia, 2019. |
dc.identifier.uri.fl_str_mv |
http://repositorio.bc.ufg.br/tede/handle/tede/10180 |
dc.identifier.dark.fl_str_mv |
ark:/38995/00130000064k7 |
identifier_str_mv |
NASCIMENTO, J. R. Problema de particionamento em subgrafos complementares: complexidade e convexidade. 2019. 129 f. Tese (Doutorado em Ciência da Computação) - Universidade Federal de Goiás, Foiânia, 2019. ark:/38995/00130000064k7 |
url |
http://repositorio.bc.ufg.br/tede/handle/tede/10180 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.program.fl_str_mv |
-3303550325223384799 |
dc.relation.confidence.fl_str_mv |
600 600 600 600 |
dc.relation.department.fl_str_mv |
-7712266734633644768 |
dc.relation.cnpq.fl_str_mv |
-8821029113617131808 |
dc.relation.sponsorship.fl_str_mv |
2075167498588264571 |
dc.rights.driver.fl_str_mv |
http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
http://creativecommons.org/licenses/by-nc-nd/4.0/ |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Universidade Federal de Goiás |
dc.publisher.program.fl_str_mv |
Programa de Pós-graduação em Ciência da Computação (INF) |
dc.publisher.initials.fl_str_mv |
UFG |
dc.publisher.country.fl_str_mv |
Brasil |
dc.publisher.department.fl_str_mv |
Instituto de Informática - INF (RG) |
publisher.none.fl_str_mv |
Universidade Federal de Goiás |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFG instname:Universidade Federal de Goiás (UFG) instacron:UFG |
instname_str |
Universidade Federal de Goiás (UFG) |
instacron_str |
UFG |
institution |
UFG |
reponame_str |
Repositório Institucional da UFG |
collection |
Repositório Institucional da UFG |
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bitstream.checksum.fl_str_mv |
bd3efa91386c1718a7f26a329fdcb468 4afdbb8c545fd630ea7db775da747b2f d41d8cd98f00b204e9800998ecf8427e d41d8cd98f00b204e9800998ecf8427e 97feaaf3fc2f24ae8f21d4c930ebd422 |
bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 MD5 |
repository.name.fl_str_mv |
Repositório Institucional da UFG - Universidade Federal de Goiás (UFG) |
repository.mail.fl_str_mv |
tasesdissertacoes.bc@ufg.br |
_version_ |
1815172574821220352 |