A computational comparison of compact MILP formulations for the zero forcing number

Detalhes bibliográficos
Autor(a) principal: Agra, Agostinho
Data de Publicação: 2019
Outros Autores: Cerdeira, Jorge Orestes, Requejo, Cristina
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://doi.org/10.1016/j.dam.2019.03.027
Resumo: UID/MAT/04106/2019. UID/MAT/00297/2019.
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spelling A computational comparison of compact MILP formulations for the zero forcing numberCompact formulationsGraphsMixed integer linear programmingValid inequalitiesZero forcingDiscrete Mathematics and CombinatoricsApplied MathematicsUID/MAT/04106/2019. UID/MAT/00297/2019.Consider a graph where some of its vertices are colored. A colored vertex with a single uncolored neighbor forces that neighbor to become colored. A zero forcing set is a set of colored vertices that forces all vertices to become colored. The zero forcing number is the size of a minimum forcing set. Finding the minimum forcing set of a graph is NP-hard. We give a new compact mixed integer linear programming formulation (MILP) for this problem, and analyze this formulation and establish relation to an existing compact formulation and to two variants. In order to solve large size instances we propose a sequential search algorithm which can also be used as a heuristic to derive upper bounds for the zero forcing number. A computational study using Xpress (a MILP solver) is conducted to test the performances of the discussed compact formulations and the sequential search algorithm. We report results on cubic, Watts–Strogatz and randomly generated graphs with 10, 20 and 30 vertices.CMA - Centro de Matemática e AplicaçõesDM - Departamento de MatemáticaRUNAgra, AgostinhoCerdeira, Jorge OrestesRequejo, Cristina2022-03-28T00:31:11Z2019-09-302019-09-30T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://doi.org/10.1016/j.dam.2019.03.027eng0166-218XPURE: 12930605http://www.scopus.com/inward/record.url?scp=85064318649&partnerID=8YFLogxKhttps://doi.org/10.1016/j.dam.2019.03.027info: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:RCAAP2024-03-11T04:35:50Zoai:run.unl.pt:10362/80892Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:35:57.701251Repositório 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 A computational comparison of compact MILP formulations for the zero forcing number
title A computational comparison of compact MILP formulations for the zero forcing number
spellingShingle A computational comparison of compact MILP formulations for the zero forcing number
Agra, Agostinho
Compact formulations
Graphs
Mixed integer linear programming
Valid inequalities
Zero forcing
Discrete Mathematics and Combinatorics
Applied Mathematics
title_short A computational comparison of compact MILP formulations for the zero forcing number
title_full A computational comparison of compact MILP formulations for the zero forcing number
title_fullStr A computational comparison of compact MILP formulations for the zero forcing number
title_full_unstemmed A computational comparison of compact MILP formulations for the zero forcing number
title_sort A computational comparison of compact MILP formulations for the zero forcing number
author Agra, Agostinho
author_facet Agra, Agostinho
Cerdeira, Jorge Orestes
Requejo, Cristina
author_role author
author2 Cerdeira, Jorge Orestes
Requejo, Cristina
author2_role author
author
dc.contributor.none.fl_str_mv CMA - Centro de Matemática e Aplicações
DM - Departamento de Matemática
RUN
dc.contributor.author.fl_str_mv Agra, Agostinho
Cerdeira, Jorge Orestes
Requejo, Cristina
dc.subject.por.fl_str_mv Compact formulations
Graphs
Mixed integer linear programming
Valid inequalities
Zero forcing
Discrete Mathematics and Combinatorics
Applied Mathematics
topic Compact formulations
Graphs
Mixed integer linear programming
Valid inequalities
Zero forcing
Discrete Mathematics and Combinatorics
Applied Mathematics
description UID/MAT/04106/2019. UID/MAT/00297/2019.
publishDate 2019
dc.date.none.fl_str_mv 2019-09-30
2019-09-30T00:00:00Z
2022-03-28T00:31:11Z
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 https://doi.org/10.1016/j.dam.2019.03.027
url https://doi.org/10.1016/j.dam.2019.03.027
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0166-218X
PURE: 12930605
http://www.scopus.com/inward/record.url?scp=85064318649&partnerID=8YFLogxK
https://doi.org/10.1016/j.dam.2019.03.027
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
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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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