The jamming constant of uniform random graphs
Resumen:
By constructing jointly a random graph and an associated exploration process, we define the dynamics of a “parking process” on a class of uniform random graphs as a measure-valued Markov process, representing the empirical degree distribution of non-explored nodes. We then establish a functional law of large numbers for this process as the number of vertices grows to infinity, allowing us to assess the jamming constant of the considered random graphs, i.e. the size of the maximal independent set discovered by the exploration algorithm. This technique, which can be applied to any uniform random graph with a given–possibly unbounded–degree distribution, can be seen as a generalization in the space of measures, of the differential equation method introduced by Wormald
| 2017 | |
|
Random graph; Configuration model Parking process Measure-valued Markov process Hydrodynamic limit Telecomunicaciones |
|
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/43556 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1807522942503878656 |
|---|---|
| author | Bermolen, Paola |
| author2 | Jonckheere, Matthieu Moyal, Pascal |
| author2_role | author author |
| author_facet | Bermolen, Paola Jonckheere, Matthieu Moyal, Pascal |
| author_role | author |
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| collection | COLIBRI |
| dc.creator.none.fl_str_mv | Bermolen, Paola Jonckheere, Matthieu Moyal, Pascal |
| dc.date.accessioned.none.fl_str_mv | 2024-04-16T16:21:31Z |
| dc.date.available.none.fl_str_mv | 2024-04-16T16:21:31Z |
| dc.date.issued.es.fl_str_mv | 2017 |
| dc.date.submitted.es.fl_str_mv | 20240416 |
| dc.description.abstract.none.fl_txt_mv | By constructing jointly a random graph and an associated exploration process, we define the dynamics of a “parking process” on a class of uniform random graphs as a measure-valued Markov process, representing the empirical degree distribution of non-explored nodes. We then establish a functional law of large numbers for this process as the number of vertices grows to infinity, allowing us to assess the jamming constant of the considered random graphs, i.e. the size of the maximal independent set discovered by the exploration algorithm. This technique, which can be applied to any uniform random graph with a given–possibly unbounded–degree distribution, can be seen as a generalization in the space of measures, of the differential equation method introduced by Wormald |
| dc.description.es.fl_txt_mv | Artículo publicado en Stochastic Processes and their Applications, v.127, no. 7, 2017, pp. 2138-2178 |
| dc.identifier.citation.es.fl_str_mv | Bermolen, P, Jonckheere, M, Moyal, P. "The jamming constant of uniform random graphs" [Preprint] Publicado en: Stochastic Processes and their Applications, v.127, no. 7, 2017, pp. 2138-2178. https://doi.org/10.1016/j.spa.2016.10.005 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/43556 |
| dc.language.iso.none.fl_str_mv | en eng |
| 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.subject.es.fl_str_mv | Random graph; Configuration model Parking process Measure-valued Markov process Hydrodynamic limit |
| dc.subject.other.es.fl_str_mv | Telecomunicaciones |
| dc.title.none.fl_str_mv | The jamming constant of uniform 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 | Artículo publicado en Stochastic Processes and their Applications, v.127, no. 7, 2017, pp. 2138-2178 |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_5b7c1312dbe4e542da24f26a3b239cc4 |
| identifier_str_mv | Bermolen, P, Jonckheere, M, Moyal, P. "The jamming constant of uniform random graphs" [Preprint] Publicado en: Stochastic Processes and their Applications, v.127, no. 7, 2017, pp. 2138-2178. https://doi.org/10.1016/j.spa.2016.10.005 |
| 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:20.500.12008/43556 |
| publishDate | 2017 |
| 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 | 2024-04-16T16:21:31Z2024-04-16T16:21:31Z201720240416Bermolen, P, Jonckheere, M, Moyal, P. "The jamming constant of uniform random graphs" [Preprint] Publicado en: Stochastic Processes and their Applications, v.127, no. 7, 2017, pp. 2138-2178. https://doi.org/10.1016/j.spa.2016.10.005https://hdl.handle.net/20.500.12008/43556Artículo publicado en Stochastic Processes and their Applications, v.127, no. 7, 2017, pp. 2138-2178By constructing jointly a random graph and an associated exploration process, we define the dynamics of a “parking process” on a class of uniform random graphs as a measure-valued Markov process, representing the empirical degree distribution of non-explored nodes. We then establish a functional law of large numbers for this process as the number of vertices grows to infinity, allowing us to assess the jamming constant of the considered random graphs, i.e. the size of the maximal independent set discovered by the exploration algorithm. This technique, which can be applied to any uniform random graph with a given–possibly unbounded–degree distribution, can be seen as a generalization in the space of measures, of the differential equation method introduced by WormaldMade available in DSpace on 2024-04-16T16:21:31Z (GMT). No. of bitstreams: 5 BJM17.pdf: 415439 bytes, checksum: 66595c2ad2c44a93dbe7d0c05c823f69 (MD5) license_text: 21936 bytes, checksum: 9833653f73f7853880c94a6fead477b1 (MD5) license_url: 49 bytes, checksum: 4afdbb8c545fd630ea7db775da747b2f (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) license.txt: 4244 bytes, checksum: 528b6a3c8c7d0c6e28129d576e989607 (MD5) Previous issue date: 2017enengLas 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)Random graph;Configuration modelParking processMeasure-valued Markov processHydrodynamic limitTelecomunicacionesThe jamming constant of uniform random graphsPreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaBermolen, PaolaJonckheere, MatthieuMoyal, PascalTelecomunicacionesAnálisis de Redes, Tráfico y Estadísticas de 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- Universidad de la Repúblicafalse |
| spellingShingle | The jamming constant of uniform random graphs Bermolen, Paola Random graph; Configuration model Parking process Measure-valued Markov process Hydrodynamic limit Telecomunicaciones |
| status_str | submittedVersion |
| title | The jamming constant of uniform random graphs |
| title_full | The jamming constant of uniform random graphs |
| title_fullStr | The jamming constant of uniform random graphs |
| title_full_unstemmed | The jamming constant of uniform random graphs |
| title_short | The jamming constant of uniform random graphs |
| title_sort | The jamming constant of uniform random graphs |
| topic | Random graph; Configuration model Parking process Measure-valued Markov process Hydrodynamic limit Telecomunicaciones |
| url | https://hdl.handle.net/20.500.12008/43556 |
