Some advances on Lovász-Schrijver semidefinite programming relaxations of the fractional stable set polytope

Autores
Bianchi, Silvia Maria; Escalante, Mariana Silvina; Nasini, Graciela Leonor; Tunçel, Levent
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study Lovász and Schrijver's hierarchy of relaxations based on positive semidefiniteness constraints derived from the fractional stable set polytope. We show that there are graphs G for which a single application of the underlying operator, N+, to the fractional stable set polytope gives a nonpolyhedral convex relaxation of the stable set polytope. We also show that none of the current best combinatorial characterizations of these relaxations obtained by a single application of the N+ operator is exact.
Fil: Bianchi, Silvia Maria. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina
Fil: Escalante, Mariana Silvina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Fil: Nasini, Graciela Leonor. 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: Tunçel, Levent. University of Waterloo; Canadá
Materia
LIFT-AND-PROJECT
SEMIDEFINITE PROGRAMMING
STABLE SET PROBLEM
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:11336/94350
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Some advances on Lovász-Schrijver semidefinite programming relaxations of the fractional stable set polytopeBianchi, Silvia MariaEscalante, Mariana SilvinaNasini, Graciela LeonorTunçel, LeventLIFT-AND-PROJECTSEMIDEFINITE PROGRAMMINGSTABLE SET PROBLEMhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study Lovász and Schrijver's hierarchy of relaxations based on positive semidefiniteness constraints derived from the fractional stable set polytope. We show that there are graphs G for which a single application of the underlying operator, N+, to the fractional stable set polytope gives a nonpolyhedral convex relaxation of the stable set polytope. We also show that none of the current best combinatorial characterizations of these relaxations obtained by a single application of the N+ operator is exact.Fil: Bianchi, Silvia Maria. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; ArgentinaFil: Escalante, Mariana Silvina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaFil: Nasini, Graciela Leonor. 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: Tunçel, Levent. University of Waterloo; CanadáElsevier Science2014-02info: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/11336/94350Bianchi, Silvia Maria; Escalante, Mariana Silvina; Nasini, Graciela Leonor; Tunçel, Levent; Some advances on Lovász-Schrijver semidefinite programming relaxations of the fractional stable set polytope; Elsevier Science; Discrete Applied Mathematics; 164; Part 2; 2-2014; 460-4690166-218XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2013.03.028info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0166218X13001765info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:19:26Zoai:ri.conicet.gov.ar:11336/94350instacron: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 11:19:26.857CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Some advances on Lovász-Schrijver semidefinite programming relaxations of the fractional stable set polytope
title Some advances on Lovász-Schrijver semidefinite programming relaxations of the fractional stable set polytope
spellingShingle Some advances on Lovász-Schrijver semidefinite programming relaxations of the fractional stable set polytope
Bianchi, Silvia Maria
LIFT-AND-PROJECT
SEMIDEFINITE PROGRAMMING
STABLE SET PROBLEM
title_short Some advances on Lovász-Schrijver semidefinite programming relaxations of the fractional stable set polytope
title_full Some advances on Lovász-Schrijver semidefinite programming relaxations of the fractional stable set polytope
title_fullStr Some advances on Lovász-Schrijver semidefinite programming relaxations of the fractional stable set polytope
title_full_unstemmed Some advances on Lovász-Schrijver semidefinite programming relaxations of the fractional stable set polytope
title_sort Some advances on Lovász-Schrijver semidefinite programming relaxations of the fractional stable set polytope
dc.creator.none.fl_str_mv Bianchi, Silvia Maria
Escalante, Mariana Silvina
Nasini, Graciela Leonor
Tunçel, Levent
author Bianchi, Silvia Maria
author_facet Bianchi, Silvia Maria
Escalante, Mariana Silvina
Nasini, Graciela Leonor
Tunçel, Levent
author_role author
author2 Escalante, Mariana Silvina
Nasini, Graciela Leonor
Tunçel, Levent
author2_role author
author
author
dc.subject.none.fl_str_mv LIFT-AND-PROJECT
SEMIDEFINITE PROGRAMMING
STABLE SET PROBLEM
topic LIFT-AND-PROJECT
SEMIDEFINITE PROGRAMMING
STABLE SET PROBLEM
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study Lovász and Schrijver's hierarchy of relaxations based on positive semidefiniteness constraints derived from the fractional stable set polytope. We show that there are graphs G for which a single application of the underlying operator, N+, to the fractional stable set polytope gives a nonpolyhedral convex relaxation of the stable set polytope. We also show that none of the current best combinatorial characterizations of these relaxations obtained by a single application of the N+ operator is exact.
Fil: Bianchi, Silvia Maria. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina
Fil: Escalante, Mariana Silvina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Fil: Nasini, Graciela Leonor. 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: Tunçel, Levent. University of Waterloo; Canadá
description We study Lovász and Schrijver's hierarchy of relaxations based on positive semidefiniteness constraints derived from the fractional stable set polytope. We show that there are graphs G for which a single application of the underlying operator, N+, to the fractional stable set polytope gives a nonpolyhedral convex relaxation of the stable set polytope. We also show that none of the current best combinatorial characterizations of these relaxations obtained by a single application of the N+ operator is exact.
publishDate 2014
dc.date.none.fl_str_mv 2014-02
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/11336/94350
Bianchi, Silvia Maria; Escalante, Mariana Silvina; Nasini, Graciela Leonor; Tunçel, Levent; Some advances on Lovász-Schrijver semidefinite programming relaxations of the fractional stable set polytope; Elsevier Science; Discrete Applied Mathematics; 164; Part 2; 2-2014; 460-469
0166-218X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/94350
identifier_str_mv Bianchi, Silvia Maria; Escalante, Mariana Silvina; Nasini, Graciela Leonor; Tunçel, Levent; Some advances on Lovász-Schrijver semidefinite programming relaxations of the fractional stable set polytope; Elsevier Science; Discrete Applied Mathematics; 164; Part 2; 2-2014; 460-469
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.2013.03.028
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0166218X13001765
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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