Asymptotic optimality of degree-greedy discovering of independent sets in Configuration Model graphs

Autores
Jonckheere, Matthieu Thimothy Samson; Sáenz, Manuel
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Finding independent sets of maximum size in fixed graphs is well known to be an NP-hard task. Using scaling limits, we characterise the asymptotics of sequential degree-greedy explorations and provide sufficient conditions for this algorithm to find an independent set of asymptotically optimal size in large sparse random graphs with given degree sequences. In the special case of sparse Erdös–Rényi graphs, our results allow to give a simple proof of the so-called e-phenomenon identified by Karp and Sipser for matchings and to give an alternative characterisation of the asymptotic independence number.
Fil: Jonckheere, Matthieu Thimothy Samson. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentina
Fil: Sáenz, Manuel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentina
Materia
HYDRODYNAMIC LIMITS
MAXIMUM INDEPENDENT SETS
RANDOM GRAPHS
SEQUENTIAL ALGORITHMS
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:11336/171213
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Asymptotic optimality of degree-greedy discovering of independent sets in Configuration Model graphsJonckheere, Matthieu Thimothy SamsonSáenz, ManuelHYDRODYNAMIC LIMITSMAXIMUM INDEPENDENT SETSRANDOM GRAPHSSEQUENTIAL ALGORITHMShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Finding independent sets of maximum size in fixed graphs is well known to be an NP-hard task. Using scaling limits, we characterise the asymptotics of sequential degree-greedy explorations and provide sufficient conditions for this algorithm to find an independent set of asymptotically optimal size in large sparse random graphs with given degree sequences. In the special case of sparse Erdös–Rényi graphs, our results allow to give a simple proof of the so-called e-phenomenon identified by Karp and Sipser for matchings and to give an alternative characterisation of the asymptotic independence number.Fil: Jonckheere, Matthieu Thimothy Samson. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; ArgentinaFil: Sáenz, Manuel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; ArgentinaElsevier Science2021-01info: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/11336/171213Jonckheere, Matthieu Thimothy Samson; Sáenz, Manuel; Asymptotic optimality of degree-greedy discovering of independent sets in Configuration Model graphs; Elsevier Science; Stochastic Processes And Their Applications; 131; 1-2021; 122-1500304-41491879-209XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0304414920303690?via%3Dihubinfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.spa.2020.09.009info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1808.10358info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:09:58Zoai:ri.conicet.gov.ar:11336/171213instacron: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 11:09:58.646CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Asymptotic optimality of degree-greedy discovering of independent sets in Configuration Model graphs
title Asymptotic optimality of degree-greedy discovering of independent sets in Configuration Model graphs
spellingShingle Asymptotic optimality of degree-greedy discovering of independent sets in Configuration Model graphs
Jonckheere, Matthieu Thimothy Samson
HYDRODYNAMIC LIMITS
MAXIMUM INDEPENDENT SETS
RANDOM GRAPHS
SEQUENTIAL ALGORITHMS
title_short Asymptotic optimality of degree-greedy discovering of independent sets in Configuration Model graphs
title_full Asymptotic optimality of degree-greedy discovering of independent sets in Configuration Model graphs
title_fullStr Asymptotic optimality of degree-greedy discovering of independent sets in Configuration Model graphs
title_full_unstemmed Asymptotic optimality of degree-greedy discovering of independent sets in Configuration Model graphs
title_sort Asymptotic optimality of degree-greedy discovering of independent sets in Configuration Model graphs
dc.creator.none.fl_str_mv Jonckheere, Matthieu Thimothy Samson
Sáenz, Manuel
author Jonckheere, Matthieu Thimothy Samson
author_facet Jonckheere, Matthieu Thimothy Samson
Sáenz, Manuel
author_role author
author2 Sáenz, Manuel
author2_role author
dc.subject.none.fl_str_mv HYDRODYNAMIC LIMITS
MAXIMUM INDEPENDENT SETS
RANDOM GRAPHS
SEQUENTIAL ALGORITHMS
topic HYDRODYNAMIC LIMITS
MAXIMUM INDEPENDENT SETS
RANDOM GRAPHS
SEQUENTIAL ALGORITHMS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Finding independent sets of maximum size in fixed graphs is well known to be an NP-hard task. Using scaling limits, we characterise the asymptotics of sequential degree-greedy explorations and provide sufficient conditions for this algorithm to find an independent set of asymptotically optimal size in large sparse random graphs with given degree sequences. In the special case of sparse Erdös–Rényi graphs, our results allow to give a simple proof of the so-called e-phenomenon identified by Karp and Sipser for matchings and to give an alternative characterisation of the asymptotic independence number.
Fil: Jonckheere, Matthieu Thimothy Samson. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentina
Fil: Sáenz, Manuel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentina
description Finding independent sets of maximum size in fixed graphs is well known to be an NP-hard task. Using scaling limits, we characterise the asymptotics of sequential degree-greedy explorations and provide sufficient conditions for this algorithm to find an independent set of asymptotically optimal size in large sparse random graphs with given degree sequences. In the special case of sparse Erdös–Rényi graphs, our results allow to give a simple proof of the so-called e-phenomenon identified by Karp and Sipser for matchings and to give an alternative characterisation of the asymptotic independence number.
publishDate 2021
dc.date.none.fl_str_mv 2021-01
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/11336/171213
Jonckheere, Matthieu Thimothy Samson; Sáenz, Manuel; Asymptotic optimality of degree-greedy discovering of independent sets in Configuration Model graphs; Elsevier Science; Stochastic Processes And Their Applications; 131; 1-2021; 122-150
0304-4149
1879-209X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/171213
identifier_str_mv Jonckheere, Matthieu Thimothy Samson; Sáenz, Manuel; Asymptotic optimality of degree-greedy discovering of independent sets in Configuration Model graphs; Elsevier Science; Stochastic Processes And Their Applications; 131; 1-2021; 122-150
0304-4149
1879-209X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0304414920303690?via%3Dihub
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.spa.2020.09.009
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1808.10358
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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