Lift-and-project ranks of the set covering polytope of circulant matrices

Autores
Bianchi, Silvia María; Escalante, Mariana Silvina; Montelar, María Susana
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we analyze the behavior of the N and N+ operators (defined by Lovász and Schrijver) and the disjunctive operator due to Balas, Ceria and Cornuéjols, on the linear relaxation of the set covering polytope associated with circulant matrices C k n . We found that for the family of circulant matrices C k sk+1 the disjunctive rank coincides with the Nand N+-rank at the value k − 1. This result provides bounds for lift-and-project ranks of most circulant matrices since C k sk+1 appears as a minor of almost all circulant matrices. According to these operators, we define the strength of facets with respect to the linear relaxation of the set covering polytope and compare the results with a similar measure previously defined by Goemans. We identify facets of maximum strength although the complete description of the set covering polytope of circulant matrices is still unknown. Moreover, considering the matrices C k sk with s ≥ k + 1, we found a family of facets of the corresponding set covering polyhedron, having maximum strength according to the disjunctive and Goemans’ measures.
Fil: Bianchi, Silvia María. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina
Fil: Escalante, Mariana Silvina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina
Fil: Montelar, María Susana. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina
Materia
CIRCULANT MATRIX
LIFT-AND-PROJECT OPERATORS
STRENGTH OF FACETS
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:11336/270734
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Lift-and-project ranks of the set covering polytope of circulant matricesBianchi, Silvia MaríaEscalante, Mariana SilvinaMontelar, María SusanaCIRCULANT MATRIXLIFT-AND-PROJECT OPERATORSSTRENGTH OF FACETShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, we analyze the behavior of the N and N+ operators (defined by Lovász and Schrijver) and the disjunctive operator due to Balas, Ceria and Cornuéjols, on the linear relaxation of the set covering polytope associated with circulant matrices C k n . We found that for the family of circulant matrices C k sk+1 the disjunctive rank coincides with the Nand N+-rank at the value k − 1. This result provides bounds for lift-and-project ranks of most circulant matrices since C k sk+1 appears as a minor of almost all circulant matrices. According to these operators, we define the strength of facets with respect to the linear relaxation of the set covering polytope and compare the results with a similar measure previously defined by Goemans. We identify facets of maximum strength although the complete description of the set covering polytope of circulant matrices is still unknown. Moreover, considering the matrices C k sk with s ≥ k + 1, we found a family of facets of the corresponding set covering polyhedron, having maximum strength according to the disjunctive and Goemans’ measures.Fil: Bianchi, Silvia María. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; ArgentinaFil: Escalante, Mariana Silvina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; ArgentinaFil: Montelar, María Susana. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; ArgentinaElsevier Science2012-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/270734Bianchi, Silvia María; Escalante, Mariana Silvina; Montelar, María Susana; Lift-and-project ranks of the set covering polytope of circulant matrices; Elsevier Science; Discrete Applied Mathematics; 160; 18; 12-2012; 2555-25620166-218XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2011.07.027info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:10:34Zoai:ri.conicet.gov.ar:11336/270734instacron: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:34982025-10-22 12:10:34.662CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Lift-and-project ranks of the set covering polytope of circulant matrices
title Lift-and-project ranks of the set covering polytope of circulant matrices
spellingShingle Lift-and-project ranks of the set covering polytope of circulant matrices
Bianchi, Silvia María
CIRCULANT MATRIX
LIFT-AND-PROJECT OPERATORS
STRENGTH OF FACETS
title_short Lift-and-project ranks of the set covering polytope of circulant matrices
title_full Lift-and-project ranks of the set covering polytope of circulant matrices
title_fullStr Lift-and-project ranks of the set covering polytope of circulant matrices
title_full_unstemmed Lift-and-project ranks of the set covering polytope of circulant matrices
title_sort Lift-and-project ranks of the set covering polytope of circulant matrices
dc.creator.none.fl_str_mv Bianchi, Silvia María
Escalante, Mariana Silvina
Montelar, María Susana
author Bianchi, Silvia María
author_facet Bianchi, Silvia María
Escalante, Mariana Silvina
Montelar, María Susana
author_role author
author2 Escalante, Mariana Silvina
Montelar, María Susana
author2_role author
author
dc.subject.none.fl_str_mv CIRCULANT MATRIX
LIFT-AND-PROJECT OPERATORS
STRENGTH OF FACETS
topic CIRCULANT MATRIX
LIFT-AND-PROJECT OPERATORS
STRENGTH OF FACETS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper, we analyze the behavior of the N and N+ operators (defined by Lovász and Schrijver) and the disjunctive operator due to Balas, Ceria and Cornuéjols, on the linear relaxation of the set covering polytope associated with circulant matrices C k n . We found that for the family of circulant matrices C k sk+1 the disjunctive rank coincides with the Nand N+-rank at the value k − 1. This result provides bounds for lift-and-project ranks of most circulant matrices since C k sk+1 appears as a minor of almost all circulant matrices. According to these operators, we define the strength of facets with respect to the linear relaxation of the set covering polytope and compare the results with a similar measure previously defined by Goemans. We identify facets of maximum strength although the complete description of the set covering polytope of circulant matrices is still unknown. Moreover, considering the matrices C k sk with s ≥ k + 1, we found a family of facets of the corresponding set covering polyhedron, having maximum strength according to the disjunctive and Goemans’ measures.
Fil: Bianchi, Silvia María. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina
Fil: Escalante, Mariana Silvina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina
Fil: Montelar, María Susana. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina
description In this paper, we analyze the behavior of the N and N+ operators (defined by Lovász and Schrijver) and the disjunctive operator due to Balas, Ceria and Cornuéjols, on the linear relaxation of the set covering polytope associated with circulant matrices C k n . We found that for the family of circulant matrices C k sk+1 the disjunctive rank coincides with the Nand N+-rank at the value k − 1. This result provides bounds for lift-and-project ranks of most circulant matrices since C k sk+1 appears as a minor of almost all circulant matrices. According to these operators, we define the strength of facets with respect to the linear relaxation of the set covering polytope and compare the results with a similar measure previously defined by Goemans. We identify facets of maximum strength although the complete description of the set covering polytope of circulant matrices is still unknown. Moreover, considering the matrices C k sk with s ≥ k + 1, we found a family of facets of the corresponding set covering polyhedron, having maximum strength according to the disjunctive and Goemans’ measures.
publishDate 2012
dc.date.none.fl_str_mv 2012-12
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/11336/270734
Bianchi, Silvia María; Escalante, Mariana Silvina; Montelar, María Susana; Lift-and-project ranks of the set covering polytope of circulant matrices; Elsevier Science; Discrete Applied Mathematics; 160; 18; 12-2012; 2555-2562
0166-218X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/270734
identifier_str_mv Bianchi, Silvia María; Escalante, Mariana Silvina; Montelar, María Susana; Lift-and-project ranks of the set covering polytope of circulant matrices; Elsevier Science; Discrete Applied Mathematics; 160; 18; 12-2012; 2555-2562
0166-218X
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.dam.2011.07.027
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
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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 12.982451

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