Sequential algorithms and independent sets discovering on large sparse random graphs.

Bermolen, Paola - Jonckheere, Matthieu - Larroca, Federico - Saenz, Manuel
Detalles Bibliográficos
2020
Inglés
Universidad de la República
COLIBRI
https://hdl.handle.net/20.500.12008/27047
Acceso abierto
Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
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author Bermolen, Paola
author2 Jonckheere, Matthieu
Larroca, Federico
Saenz, Manuel
author2_role author
author
author
author_facet Bermolen, Paola
Jonckheere, Matthieu
Larroca, Federico
Saenz, Manuel
author_role author
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dc.contributor.filiacion.none.fl_str_mv Bermolen Paola, Universidad de la República (Uruguay). Facultad de Ingeniería.
Jonckheere Matthieu, Instituto de Cálculo, UBA/CONICET, Buenos Aires, Argentina
Larroca Federico, Universidad de la República (Uruguay). Facultad de Ingeniería.
Saenz Manuel, Instituto de Cálculo, UBA/CONICET, Buenos Aires, Argentina
dc.creator.none.fl_str_mv Bermolen, Paola
Jonckheere, Matthieu
Larroca, Federico
Saenz, Manuel
dc.date.accessioned.none.fl_str_mv 2021-04-12T18:34:49Z
dc.date.available.none.fl_str_mv 2021-04-12T18:34:49Z
dc.date.issued.none.fl_str_mv 2020
dc.description.en.fl_txt_mv Computing the size of maximum independent sets is a NP-hard problem for fixed graphs. Characterizing and designing efficient algorithms to estimate this independence number for random graphs are notoriously difficult and still largely open issues. In a companion paper, we showed that a low complexity degree-greedy exploration is actually asymptotically optimal on a large class of sparse random graphs. Encouraged by this result, we present and study two variants of sequential exploration algorithms: static and dynamic degree-aware explorations. We derive hydrodynamic limits for both of them, which in turn allow us to compute the size of the resulting independent set. Whereas the former is simpler to compute, the latter may be used to arbitrarily approximate the degree-greedy algorithm. Both can be implemented in a distributed manner. The corresponding hydrodynamic limits constitute an efficient method to compute or bound the independence number for a large class of sparse random graphs. As an application, we then show how our method may be used to estimate the capacity of a large 802.11-based wireless network. We finally consider further indicators such as the fairness of the resulting configuration, and show how an unexpected trade-off between fairness and capacity can be achieved.
dc.format.extent.es.fl_str_mv 29 p.
dc.format.mimetype.es.fl_str_mv application/pdf
dc.identifier.citation.es.fl_str_mv Bermolen, P., Jonckheere, M., Larroca, F. y otros. Sequential algorithms and independent sets discovering on large sparse random graphs [Preprint]. EN: Mathematics (math.PR-Probability), 2020, pp 1-.29. arXiv:2009.14574.
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12008/27047
dc.language.iso.none.fl_str_mv en
eng
dc.publisher.es.fl_str_mv arXiv
dc.relation.ispartof.es.fl_str_mv Mathematics (math.PR-Probability), arXiv:2009.14574, pp 1-29, Sep 2020
dc.rights.license.none.fl_str_mv Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
dc.source.none.fl_str_mv reponame:COLIBRI
instname:Universidad de la República
instacron:Universidad de la República
dc.title.none.fl_str_mv Sequential algorithms and independent sets discovering on large sparse random graphs.
dc.type.es.fl_str_mv Preprint
dc.type.none.fl_str_mv info:eu-repo/semantics/preprint
dc.type.version.none.fl_str_mv info:eu-repo/semantics/submittedVersion
description Computing the size of maximum independent sets is a NP-hard problem for fixed graphs. Characterizing and designing efficient algorithms to estimate this independence number for random graphs are notoriously difficult and still largely open issues. In a companion paper, we showed that a low complexity degree-greedy exploration is actually asymptotically optimal on a large class of sparse random graphs. Encouraged by this result, we present and study two variants of sequential exploration algorithms: static and dynamic degree-aware explorations. We derive hydrodynamic limits for both of them, which in turn allow us to compute the size of the resulting independent set. Whereas the former is simpler to compute, the latter may be used to arbitrarily approximate the degree-greedy algorithm. Both can be implemented in a distributed manner. The corresponding hydrodynamic limits constitute an efficient method to compute or bound the independence number for a large class of sparse random graphs. As an application, we then show how our method may be used to estimate the capacity of a large 802.11-based wireless network. We finally consider further indicators such as the fairness of the resulting configuration, and show how an unexpected trade-off between fairness and capacity can be achieved.
eu_rights_str_mv openAccess
format preprint
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identifier_str_mv Bermolen, P., Jonckheere, M., Larroca, F. y otros. Sequential algorithms and independent sets discovering on large sparse random graphs [Preprint]. EN: Mathematics (math.PR-Probability), 2020, pp 1-.29. arXiv:2009.14574.
instacron_str Universidad de la República
institution Universidad de la República
instname_str Universidad de la República
language eng
language_invalid_str_mv en
network_acronym_str COLIBRI
network_name_str COLIBRI
oai_identifier_str oai:colibri.udelar.edu.uy:20.500.12008/27047
publishDate 2020
reponame_str COLIBRI
repository.mail.fl_str_mv mabel.seroubian@seciu.edu.uy
repository.name.fl_str_mv COLIBRI - Universidad de la República
repository_id_str 4771
rights_invalid_str_mv Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
spelling Bermolen Paola, Universidad de la República (Uruguay). Facultad de Ingeniería.Jonckheere Matthieu, Instituto de Cálculo, UBA/CONICET, Buenos Aires, ArgentinaLarroca Federico, Universidad de la República (Uruguay). Facultad de Ingeniería.Saenz Manuel, Instituto de Cálculo, UBA/CONICET, Buenos Aires, Argentina2021-04-12T18:34:49Z2021-04-12T18:34:49Z2020Bermolen, P., Jonckheere, M., Larroca, F. y otros. Sequential algorithms and independent sets discovering on large sparse random graphs [Preprint]. EN: Mathematics (math.PR-Probability), 2020, pp 1-.29. arXiv:2009.14574.https://hdl.handle.net/20.500.12008/27047Computing the size of maximum independent sets is a NP-hard problem for fixed graphs. Characterizing and designing efficient algorithms to estimate this independence number for random graphs are notoriously difficult and still largely open issues. In a companion paper, we showed that a low complexity degree-greedy exploration is actually asymptotically optimal on a large class of sparse random graphs. Encouraged by this result, we present and study two variants of sequential exploration algorithms: static and dynamic degree-aware explorations. We derive hydrodynamic limits for both of them, which in turn allow us to compute the size of the resulting independent set. Whereas the former is simpler to compute, the latter may be used to arbitrarily approximate the degree-greedy algorithm. Both can be implemented in a distributed manner. The corresponding hydrodynamic limits constitute an efficient method to compute or bound the independence number for a large class of sparse random graphs. As an application, we then show how our method may be used to estimate the capacity of a large 802.11-based wireless network. We finally consider further indicators such as the fairness of the resulting configuration, and show how an unexpected trade-off between fairness and capacity can be achieved.Submitted by Ribeiro Jorge (jribeiro@fing.edu.uy) on 2021-04-11T04:59:55Z No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) BJLS20.pdf: 2167225 bytes, checksum: 86c497bbc084e5fccd9aa4e777e55856 (MD5)Approved for entry into archive by Machado Jimena (jmachado@fing.edu.uy) on 2021-04-12T18:03:51Z (GMT) No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) BJLS20.pdf: 2167225 bytes, checksum: 86c497bbc084e5fccd9aa4e777e55856 (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@fic.edu.uy) on 2021-04-12T18:34:49Z (GMT). No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) BJLS20.pdf: 2167225 bytes, checksum: 86c497bbc084e5fccd9aa4e777e55856 (MD5) Previous issue date: 202029 p.application/pdfenengarXivMathematics (math.PR-Probability), arXiv:2009.14574, pp 1-29, Sep 2020Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)Sequential algorithms and independent sets discovering on large sparse random graphs.Preprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaBermolen, PaolaJonckheere, MatthieuLarroca, FedericoSaenz, ManuelLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/27047/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/27047/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; charset=utf-838616http://localhost:8080/xmlui/bitstream/20.500.12008/27047/3/license_text36c32e9c6da50e6d55578c16944ef7f6MD53license_rdflicense_rdfapplication/rdf+xml; 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- Universidad de la Repúblicafalse
spellingShingle Sequential algorithms and independent sets discovering on large sparse random graphs.
Bermolen, Paola
status_str submittedVersion
title Sequential algorithms and independent sets discovering on large sparse random graphs.
title_full Sequential algorithms and independent sets discovering on large sparse random graphs.
title_fullStr Sequential algorithms and independent sets discovering on large sparse random graphs.
title_full_unstemmed Sequential algorithms and independent sets discovering on large sparse random graphs.
title_short Sequential algorithms and independent sets discovering on large sparse random graphs.
title_sort Sequential algorithms and independent sets discovering on large sparse random graphs.
url https://hdl.handle.net/20.500.12008/27047

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