Combinatorial Flexibility problems and their computational Complexity

Autores
Aguilera, Néstor Edgardo; Leoni, Valeria Alejandra; Nasini, Graciela Leonor
Año de publicación
2008
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The concept of flexibility-originated in the context of heat exchanger networks-is associated with a substructure which guarantees the performance of the original structure, in a given range of possible states. We extend this concept to combinatorial optimization problems, and prove several computational complexity results in this new framework. Under some monotonicity conditions, we prove that a combinatorial optimization problem polynomially transforms to its associated flexibility problem, but that the converse need not be true. In order to obtain polynomial flexibility problems, we have to restrict ourselves to combinatorial optimization problems on matroids. We also prove that, when relaxing in different ways the matroid structure, the flexibility problems become NP-complete. This fact is shown by proving the NP-completeness of the flexibility problems associated with the Shortest Path, Minimum Cut and Weighted Matching problems.
Fil: Aguilera, Néstor Edgardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Leoni, Valeria Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario; Argentina
Fil: Nasini, Graciela Leonor. Universidad Nacional de Rosario; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Materia
COMBINATORIAL PROBLEMS
COMPUTATIONAL COMPLEXITY
FLEXIBILITY
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/84281
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Combinatorial Flexibility problems and their computational ComplexityAguilera, Néstor EdgardoLeoni, Valeria AlejandraNasini, Graciela LeonorCOMBINATORIAL PROBLEMSCOMPUTATIONAL COMPLEXITYFLEXIBILITYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The concept of flexibility-originated in the context of heat exchanger networks-is associated with a substructure which guarantees the performance of the original structure, in a given range of possible states. We extend this concept to combinatorial optimization problems, and prove several computational complexity results in this new framework. Under some monotonicity conditions, we prove that a combinatorial optimization problem polynomially transforms to its associated flexibility problem, but that the converse need not be true. In order to obtain polynomial flexibility problems, we have to restrict ourselves to combinatorial optimization problems on matroids. We also prove that, when relaxing in different ways the matroid structure, the flexibility problems become NP-complete. This fact is shown by proving the NP-completeness of the flexibility problems associated with the Shortest Path, Minimum Cut and Weighted Matching problems.Fil: Aguilera, Néstor Edgardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Leoni, Valeria Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario; ArgentinaFil: Nasini, Graciela Leonor. Universidad Nacional de Rosario; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaElsevier2008-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/84281Aguilera, Néstor Edgardo; Leoni, Valeria Alejandra; Nasini, Graciela Leonor; Combinatorial Flexibility problems and their computational Complexity; Elsevier; Electronic Notes in Discrete Mathematics; 30; C; 2-2008; 303-3081571-0653CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.endm.2008.01.052info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-17T11:45:41Zoai:ri.conicet.gov.ar:11336/84281instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-17 11:45:41.787CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Combinatorial Flexibility problems and their computational Complexity
title Combinatorial Flexibility problems and their computational Complexity
spellingShingle Combinatorial Flexibility problems and their computational Complexity
Aguilera, Néstor Edgardo
COMBINATORIAL PROBLEMS
COMPUTATIONAL COMPLEXITY
FLEXIBILITY
title_short Combinatorial Flexibility problems and their computational Complexity
title_full Combinatorial Flexibility problems and their computational Complexity
title_fullStr Combinatorial Flexibility problems and their computational Complexity
title_full_unstemmed Combinatorial Flexibility problems and their computational Complexity
title_sort Combinatorial Flexibility problems and their computational Complexity
dc.creator.none.fl_str_mv Aguilera, Néstor Edgardo
Leoni, Valeria Alejandra
Nasini, Graciela Leonor
author Aguilera, Néstor Edgardo
author_facet Aguilera, Néstor Edgardo
Leoni, Valeria Alejandra
Nasini, Graciela Leonor
author_role author
author2 Leoni, Valeria Alejandra
Nasini, Graciela Leonor
author2_role author
author
dc.subject.none.fl_str_mv COMBINATORIAL PROBLEMS
COMPUTATIONAL COMPLEXITY
FLEXIBILITY
topic COMBINATORIAL PROBLEMS
COMPUTATIONAL COMPLEXITY
FLEXIBILITY
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The concept of flexibility-originated in the context of heat exchanger networks-is associated with a substructure which guarantees the performance of the original structure, in a given range of possible states. We extend this concept to combinatorial optimization problems, and prove several computational complexity results in this new framework. Under some monotonicity conditions, we prove that a combinatorial optimization problem polynomially transforms to its associated flexibility problem, but that the converse need not be true. In order to obtain polynomial flexibility problems, we have to restrict ourselves to combinatorial optimization problems on matroids. We also prove that, when relaxing in different ways the matroid structure, the flexibility problems become NP-complete. This fact is shown by proving the NP-completeness of the flexibility problems associated with the Shortest Path, Minimum Cut and Weighted Matching problems.
Fil: Aguilera, Néstor Edgardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Leoni, Valeria Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario; Argentina
Fil: Nasini, Graciela Leonor. Universidad Nacional de Rosario; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
description The concept of flexibility-originated in the context of heat exchanger networks-is associated with a substructure which guarantees the performance of the original structure, in a given range of possible states. We extend this concept to combinatorial optimization problems, and prove several computational complexity results in this new framework. Under some monotonicity conditions, we prove that a combinatorial optimization problem polynomially transforms to its associated flexibility problem, but that the converse need not be true. In order to obtain polynomial flexibility problems, we have to restrict ourselves to combinatorial optimization problems on matroids. We also prove that, when relaxing in different ways the matroid structure, the flexibility problems become NP-complete. This fact is shown by proving the NP-completeness of the flexibility problems associated with the Shortest Path, Minimum Cut and Weighted Matching problems.
publishDate 2008
dc.date.none.fl_str_mv 2008-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/84281
Aguilera, Néstor Edgardo; Leoni, Valeria Alejandra; Nasini, Graciela Leonor; Combinatorial Flexibility problems and their computational Complexity; Elsevier; Electronic Notes in Discrete Mathematics; 30; C; 2-2008; 303-308
1571-0653
CONICET Digital
CONICET
url http://hdl.handle.net/11336/84281
identifier_str_mv Aguilera, Néstor Edgardo; Leoni, Valeria Alejandra; Nasini, Graciela Leonor; Combinatorial Flexibility problems and their computational Complexity; Elsevier; Electronic Notes in Discrete Mathematics; 30; C; 2-2008; 303-308
1571-0653
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.endm.2008.01.052
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.001348

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