Large deviation principle for the Greedy exploration algorithm over Erdös-Rényi graphs
Resumen:
We prove a large deviation principle for a greedy exploration process on an Erdös-Rényi (ER) graph when the number of nodes goes to infinity. To prove our main result, we use the general strategy to study large deviations of processes proposed by Feng and Kurtz (2006), based on the convergence of non-linear semigroups. The rate function can be expressed in a closed-form formula, and associated optimization problems can be solved explicitly, providing the large deviation trajectory. Also, we derive large deviation results for the size of the maximum independent set discovered by such an algorithm and analyse the probability that it exceeds known bounds for the maximal independent set. We also analyse the link between these results and the landscape complexity of the independent set and the exploration dynamic
| 2022 | |
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Large deviation principle Greedy exploration algorithms Erdös-Rényi Graphs Comparison principle. Hamilton-Jacobi equations |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/41045 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1807522801553244160 |
|---|---|
| author | Bermolen, Paola |
| author2 | Goicoechea Jackson, Valeria Jonckheere, Matthieu Mordecki, Ernesto |
| author2_role | author author author |
| author_facet | Bermolen, Paola Goicoechea Jackson, Valeria Jonckheere, Matthieu Mordecki, Ernesto |
| author_role | author |
| bitstream.checksum.fl_str_mv | 6429389a7df7277b72b7924fdc7d47a9 a006180e3f5b2ad0b88185d14284c0e0 6eed504571858d3e58aeed5ad67e191a 489f03e71d39068f329bdec8798bce58 bb291069abc69c07e5a5d3163565b67d |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Bermolen Paola, Universidad de la República (Uruguay). Facultad de Ingeniería. Goicoechea Jackson Valeria, Universidad de la República (Uruguay). Facultad de Ingeniería. Jonckheere Matthieu, Universidad de la República (Uruguay). Facultad de Ingeniería. Mordecki Ernesto, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. |
| dc.creator.none.fl_str_mv | Bermolen, Paola Goicoechea Jackson, Valeria Jonckheere, Matthieu Mordecki, Ernesto |
| dc.date.accessioned.none.fl_str_mv | 2023-11-10T14:12:13Z |
| dc.date.available.none.fl_str_mv | 2023-11-10T14:12:13Z |
| dc.date.issued.none.fl_str_mv | 2022 |
| dc.description.abstract.none.fl_txt_mv | We prove a large deviation principle for a greedy exploration process on an Erdös-Rényi (ER) graph when the number of nodes goes to infinity. To prove our main result, we use the general strategy to study large deviations of processes proposed by Feng and Kurtz (2006), based on the convergence of non-linear semigroups. The rate function can be expressed in a closed-form formula, and associated optimization problems can be solved explicitly, providing the large deviation trajectory. Also, we derive large deviation results for the size of the maximum independent set discovered by such an algorithm and analyse the probability that it exceeds known bounds for the maximal independent set. We also analyse the link between these results and the landscape complexity of the independent set and the exploration dynamic |
| dc.format.extent.es.fl_str_mv | 18 h. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Bermolen, P, Goicoechea Jackson, V, Jonckheere, M [y otro autor]. "Large deviation principle for the Greedy exploration algorithm over Erdös-Rényi graphs". Latin American Journal of Probability and Mathematical Statistics. [en línea] 2022, 19: 439-456. 18 h. DOI: 10.30757/ALEA.v19-16 |
| dc.identifier.doi.none.fl_str_mv | 10.30757/ALEA.v19-16 |
| dc.identifier.issn.none.fl_str_mv | 1980-0436 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/41045 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | ALEA |
| dc.relation.ispartof.es.fl_str_mv | Latin American Journal of Probability and Mathematical Statistics, 2022, 19: 439-456 |
| 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 | Large deviation principle Greedy exploration algorithms Erdös-Rényi Graphs Comparison principle. Hamilton-Jacobi equations |
| dc.title.none.fl_str_mv | Large deviation principle for the Greedy exploration algorithm over Erdös-Rényi graphs |
| dc.type.es.fl_str_mv | Artículo |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/article |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/publishedVersion |
| description | We prove a large deviation principle for a greedy exploration process on an Erdös-Rényi (ER) graph when the number of nodes goes to infinity. To prove our main result, we use the general strategy to study large deviations of processes proposed by Feng and Kurtz (2006), based on the convergence of non-linear semigroups. The rate function can be expressed in a closed-form formula, and associated optimization problems can be solved explicitly, providing the large deviation trajectory. Also, we derive large deviation results for the size of the maximum independent set discovered by such an algorithm and analyse the probability that it exceeds known bounds for the maximal independent set. We also analyse the link between these results and the landscape complexity of the independent set and the exploration dynamic |
| eu_rights_str_mv | openAccess |
| format | article |
| id | COLIBRI_d696b07088a8d907d07c42828f34e1f3 |
| identifier_str_mv | Bermolen, P, Goicoechea Jackson, V, Jonckheere, M [y otro autor]. "Large deviation principle for the Greedy exploration algorithm over Erdös-Rényi graphs". Latin American Journal of Probability and Mathematical Statistics. [en línea] 2022, 19: 439-456. 18 h. DOI: 10.30757/ALEA.v19-16 1980-0436 10.30757/ALEA.v19-16 |
| 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:20.500.12008/41045 |
| publishDate | 2022 |
| 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.Goicoechea Jackson Valeria, Universidad de la República (Uruguay). Facultad de Ingeniería.Jonckheere Matthieu, Universidad de la República (Uruguay). Facultad de Ingeniería.Mordecki Ernesto, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.2023-11-10T14:12:13Z2023-11-10T14:12:13Z2022Bermolen, P, Goicoechea Jackson, V, Jonckheere, M [y otro autor]. "Large deviation principle for the Greedy exploration algorithm over Erdös-Rényi graphs". Latin American Journal of Probability and Mathematical Statistics. [en línea] 2022, 19: 439-456. 18 h. DOI: 10.30757/ALEA.v19-161980-0436https://hdl.handle.net/20.500.12008/4104510.30757/ALEA.v19-16We prove a large deviation principle for a greedy exploration process on an Erdös-Rényi (ER) graph when the number of nodes goes to infinity. To prove our main result, we use the general strategy to study large deviations of processes proposed by Feng and Kurtz (2006), based on the convergence of non-linear semigroups. The rate function can be expressed in a closed-form formula, and associated optimization problems can be solved explicitly, providing the large deviation trajectory. Also, we derive large deviation results for the size of the maximum independent set discovered by such an algorithm and analyse the probability that it exceeds known bounds for the maximal independent set. We also analyse the link between these results and the landscape complexity of the independent set and the exploration dynamicSubmitted by Egaña Florencia (florega@gmail.com) on 2023-11-09T18:09:05Z No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 19-16.pdf: 693137 bytes, checksum: bb291069abc69c07e5a5d3163565b67d (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2023-11-10T13:26:14Z (GMT) No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 19-16.pdf: 693137 bytes, checksum: bb291069abc69c07e5a5d3163565b67d (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2023-11-10T14:12:13Z (GMT). No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 19-16.pdf: 693137 bytes, checksum: bb291069abc69c07e5a5d3163565b67d (MD5) Previous issue date: 202218 h.application/pdfenengALEALatin American Journal of Probability and Mathematical Statistics, 2022, 19: 439-456Las 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)Large deviation principleGreedy exploration algorithmsErdös-Rényi GraphsComparison principle.Hamilton-Jacobi equationsLarge deviation principle for the Greedy exploration algorithm over Erdös-Rényi graphsArtículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaBermolen, PaolaGoicoechea Jackson, ValeriaJonckheere, MatthieuMordecki, ErnestoLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/41045/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/41045/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse |
| spellingShingle | Large deviation principle for the Greedy exploration algorithm over Erdös-Rényi graphs Bermolen, Paola Large deviation principle Greedy exploration algorithms Erdös-Rényi Graphs Comparison principle. Hamilton-Jacobi equations |
| status_str | publishedVersion |
| title | Large deviation principle for the Greedy exploration algorithm over Erdös-Rényi graphs |
| title_full | Large deviation principle for the Greedy exploration algorithm over Erdös-Rényi graphs |
| title_fullStr | Large deviation principle for the Greedy exploration algorithm over Erdös-Rényi graphs |
| title_full_unstemmed | Large deviation principle for the Greedy exploration algorithm over Erdös-Rényi graphs |
| title_short | Large deviation principle for the Greedy exploration algorithm over Erdös-Rényi graphs |
| title_sort | Large deviation principle for the Greedy exploration algorithm over Erdös-Rényi graphs |
| topic | Large deviation principle Greedy exploration algorithms Erdös-Rényi Graphs Comparison principle. Hamilton-Jacobi equations |
| url | https://hdl.handle.net/20.500.12008/41045 |
