Problema de particionamento em subgrafos complementares: complexidade e convexidade

Detalhes bibliográficos
Autor(a) principal: Nascimento, Julliano Rosa
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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spelling 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
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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
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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
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