The max-out min-in problem

Detalhes bibliográficos
Autor(a) principal: Cerdeira, Jorge Orestes
Data de Publicação: 2023
Outros Autores: Martins, Maria João, Raydan, Marcos
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/153372
Resumo: Funding Information: The first and third authors were financially supported by the Fundação para a Ciência e a Tecnologia, Portugal (Portuguese Foundation for Science and Technology) through the projects UIDB/MAT/00297/2020 , UIDP/MAT/00297/2020 (Centro de Matemática e Aplicações). Publisher Copyright: © 2023 The Author(s)
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spelling The max-out min-in problemA tool for data analysisCluster analysisCombinatorial optimizationComputational complexityQuadratic programmingVariable selectionWeighted graphsComputer Science(all)Modelling and SimulationManagement Science and Operations ResearchFunding Information: The first and third authors were financially supported by the Fundação para a Ciência e a Tecnologia, Portugal (Portuguese Foundation for Science and Technology) through the projects UIDB/MAT/00297/2020 , UIDP/MAT/00297/2020 (Centro de Matemática e Aplicações). Publisher Copyright: © 2023 The Author(s)Consider a graph with vertex set V and non-negative weights on the edges. For every subset of vertices S, define ϕ(S) to be the sum of the weights of edges with one vertex in S and the other in V∖S, minus the sum of the weights of the edges with both vertices in S. We consider the problem of finding S⊆V for which ϕ(S) is maximized. We call this combinatorial optimization problem the max-out min-in problem (MOMIP). In this paper we (i) present a linear 0/1 formulation and a quadratic unconstrained binary optimization formulation for MOMIP; (ii) prove that the problem is NP-hard; (iii) report results of computational experiments on simulated data to compare the performances of the two models; (iv) illustrate the applicability of MOMIP for two different topics in the context of data analysis, namely in the selection of variables in exploratory data analysis and in the identification of clusters in the context of cluster analysis; and (v) introduce a generalization of MOMIP that includes, as particular cases, the well-known weighted maximum cut problem and a novel problem related to independent dominant sets in graphs.DM - Departamento de MatemáticaCMA - Centro de Matemática e AplicaçõesRUNCerdeira, Jorge OrestesMartins, Maria JoãoRaydan, Marcos2023-05-30T22:23:16Z2023-062023-06-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article11application/pdfhttp://hdl.handle.net/10362/153372eng0305-0548PURE: 62047403https://doi.org/10.1016/j.cor.2023.106218info: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:RCAAP2024-03-11T05:35:55Zoai:run.unl.pt:10362/153372Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:55:15.872055Repositório 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 The max-out min-in problem
A tool for data analysis
title The max-out min-in problem
spellingShingle The max-out min-in problem
Cerdeira, Jorge Orestes
Cluster analysis
Combinatorial optimization
Computational complexity
Quadratic programming
Variable selection
Weighted graphs
Computer Science(all)
Modelling and Simulation
Management Science and Operations Research
title_short The max-out min-in problem
title_full The max-out min-in problem
title_fullStr The max-out min-in problem
title_full_unstemmed The max-out min-in problem
title_sort The max-out min-in problem
author Cerdeira, Jorge Orestes
author_facet Cerdeira, Jorge Orestes
Martins, Maria João
Raydan, Marcos
author_role author
author2 Martins, Maria João
Raydan, Marcos
author2_role author
author
dc.contributor.none.fl_str_mv DM - Departamento de Matemática
CMA - Centro de Matemática e Aplicações
RUN
dc.contributor.author.fl_str_mv Cerdeira, Jorge Orestes
Martins, Maria João
Raydan, Marcos
dc.subject.por.fl_str_mv Cluster analysis
Combinatorial optimization
Computational complexity
Quadratic programming
Variable selection
Weighted graphs
Computer Science(all)
Modelling and Simulation
Management Science and Operations Research
topic Cluster analysis
Combinatorial optimization
Computational complexity
Quadratic programming
Variable selection
Weighted graphs
Computer Science(all)
Modelling and Simulation
Management Science and Operations Research
description Funding Information: The first and third authors were financially supported by the Fundação para a Ciência e a Tecnologia, Portugal (Portuguese Foundation for Science and Technology) through the projects UIDB/MAT/00297/2020 , UIDP/MAT/00297/2020 (Centro de Matemática e Aplicações). Publisher Copyright: © 2023 The Author(s)
publishDate 2023
dc.date.none.fl_str_mv 2023-05-30T22:23:16Z
2023-06
2023-06-01T00:00:00Z
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 http://hdl.handle.net/10362/153372
url http://hdl.handle.net/10362/153372
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0305-0548
PURE: 62047403
https://doi.org/10.1016/j.cor.2023.106218
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 11
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
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