Analysis of Formulations for the Cluster Partitioning Problem

Detalhes bibliográficos
Autor(a) principal: Silva, Mafalda Leal Saudade e
Data de Publicação: 2022
Tipo de documento: Dissertação
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10451/58983
Resumo: Tese de mestrado, Estatística e Investigação Operacional (Investigação Operacional), 2022, Universidade de Lisboa, Faculdade de Ciências
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spelling Analysis of Formulations for the Cluster Partitioning Problemk-plexgrafopartiçãorelaxações de cliquesTeses de mestrado - 2022Departamento de Estatística e Investigação OperacionalTese de mestrado, Estatística e Investigação Operacional (Investigação Operacional), 2022, Universidade de Lisboa, Faculdade de CiênciasA graph is an abstract structure that is frequently used to model interpersonal relationships and/or social interactions. Since relationships between individuals are frequently represented by graphs, it makes sense to utilise graphs to look for groups of those individuals. These clusters are best modelled as cliques, however when it is necessary to represent the underlying issues when the amount of cohesion required is less than the level imposed by a clique, relaxed versions of those clusters may be taken into consideration. The k-plex relaxation is the one being examined in this project. Most of the formulations proposed in the literature aim to solve the Maximum Clique Problem or the Graph Partitioning Problem. The Cluster Partitioning Problem is known as the problem of partitioning a graph’s nodes into distinct clusters. This problem can be viewed as a specific case of the general Graph Partitioning Problem, where each set within the partition must respect certain requirements depending on the type of cluster being considered. In the present project, three formulations were proposed to solve the Cluster Partitioning Problem when the clusters being considered are k-plexes. These formulations were based on formulations proposed for the Maximum K-plex Problem and for the K-Plex Partitioning Problem taking into consideration different objective functions. Furthermore, improvements and extended formulations were presented for these models. Three sets of instances were considered to evaluate the performance of each model. Computational results show that when comparing the three base formulations, the Coneighbourhood Model presents the best results for the first objective function studied and the Complementary Edge Model and the Cluster Representative Model present the best solutions for the second objective function studied. However, when enhancements and extended formulations are introduced, it can be concluded that for both objective functions the Linearised Extended Cluster Representative Model is the one that produces the overall best results for the instances studied.Telhada, João Miguel Paixão, 1971-Repositório da Universidade de LisboaSilva, Mafalda Leal Saudade e2023-08-24T10:02:33Z202220222022-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisapplication/pdfhttp://hdl.handle.net/10451/58983enginfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-08T17:07:57Zoai:repositorio.ul.pt:10451/58983Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:09:02.224356Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Analysis of Formulations for the Cluster Partitioning Problem
title Analysis of Formulations for the Cluster Partitioning Problem
spellingShingle Analysis of Formulations for the Cluster Partitioning Problem
Silva, Mafalda Leal Saudade e
k-plex
grafo
partição
relaxações de cliques
Teses de mestrado - 2022
Departamento de Estatística e Investigação Operacional
title_short Analysis of Formulations for the Cluster Partitioning Problem
title_full Analysis of Formulations for the Cluster Partitioning Problem
title_fullStr Analysis of Formulations for the Cluster Partitioning Problem
title_full_unstemmed Analysis of Formulations for the Cluster Partitioning Problem
title_sort Analysis of Formulations for the Cluster Partitioning Problem
author Silva, Mafalda Leal Saudade e
author_facet Silva, Mafalda Leal Saudade e
author_role author
dc.contributor.none.fl_str_mv Telhada, João Miguel Paixão, 1971-
Repositório da Universidade de Lisboa
dc.contributor.author.fl_str_mv Silva, Mafalda Leal Saudade e
dc.subject.por.fl_str_mv k-plex
grafo
partição
relaxações de cliques
Teses de mestrado - 2022
Departamento de Estatística e Investigação Operacional
topic k-plex
grafo
partição
relaxações de cliques
Teses de mestrado - 2022
Departamento de Estatística e Investigação Operacional
description Tese de mestrado, Estatística e Investigação Operacional (Investigação Operacional), 2022, Universidade de Lisboa, Faculdade de Ciências
publishDate 2022
dc.date.none.fl_str_mv 2022
2022
2022-01-01T00:00:00Z
2023-08-24T10:02:33Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10451/58983
url http://hdl.handle.net/10451/58983
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
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