The max-out min-in problem
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Outros Autores: | , |
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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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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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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1799138140130115584 |