Uniformly Optimally Reliable Graphs: A Survey
Resumen:
Which is the most reliable graph with n nodes and m edges? This celebrated problem has several aspects, according to the notion of optimality (in a local or uniform sense), failure type (either nodes or edges), or reliability model (all-terminal connectedness, two-terminal or multiterminal setting). This article presents a chronological survey of the multiple proposals to address the problem, together with recent trends and enigmatic conjectures posed decades ago that promote further research.
| 2021 | |
| Agencia Nacional de Investigación e Innovación | |
|
Uniformly most reliable graph Uniformly least reliable graph All-terminal reliability Two-terminal reliability Failure type Graph theory Ciencias Naturales y Exactas Matemáticas Matemática Aplicada |
|
| Inglés | |
| Agencia Nacional de Investigación e Innovación | |
| REDI | |
| https://hdl.handle.net/20.500.12381/699 | |
| Acceso abierto | |
| Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional. (CC BY-NC-ND) |
| _version_ | 1814959256244322304 |
|---|---|
| author | Romero, Pablo |
| author_facet | Romero, Pablo |
| author_role | author |
| bitstream.checksum.fl_str_mv | 3c9d86d36485746409b4281a0893d729 0cd7d61180725b15d5ee832302829f37 |
| bitstream.checksumAlgorithm.fl_str_mv | MD5 MD5 |
| bitstream.url.fl_str_mv | https://redi.anii.org.uy/jspui/bitstream/20.500.12381/699/2/license.txt https://redi.anii.org.uy/jspui/bitstream/20.500.12381/699/1/1%20%281%29.pdf |
| collection | REDI |
| dc.creator.none.fl_str_mv | Romero, Pablo |
| dc.date.accessioned.none.fl_str_mv | 2022-10-20T23:26:20Z |
| dc.date.issued.none.fl_str_mv | 2021-12-06 |
| dc.description.abstract.none.fl_txt_mv | Which is the most reliable graph with n nodes and m edges? This celebrated problem has several aspects, according to the notion of optimality (in a local or uniform sense), failure type (either nodes or edges), or reliability model (all-terminal connectedness, two-terminal or multiterminal setting). This article presents a chronological survey of the multiple proposals to address the problem, together with recent trends and enigmatic conjectures posed decades ago that promote further research. |
| dc.description.sponsorship.none.fl_txt_mv | Agencia Nacional de Investigación e Innovación |
| dc.identifier.anii.es.fl_str_mv | FCE_1_2019_1_156693 |
| dc.identifier.doi.none.fl_str_mv | 10.1002/net.22085 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12381/699 |
| dc.language.iso.none.fl_str_mv | eng |
| dc.publisher.es.fl_str_mv | Wiley |
| dc.rights.embargoterm.es.fl_str_mv | 2022-12-06 |
| dc.rights.es.fl_str_mv | Acceso abierto |
| dc.rights.license.none.fl_str_mv | Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional. (CC BY-NC-ND) |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.es.fl_str_mv | Networks |
| dc.source.none.fl_str_mv | reponame:REDI instname:Agencia Nacional de Investigación e Innovación instacron:Agencia Nacional de Investigación e Innovación |
| dc.subject.anii.none.fl_str_mv | Ciencias Naturales y Exactas Matemáticas Matemática Aplicada |
| dc.subject.es.fl_str_mv | Uniformly most reliable graph Uniformly least reliable graph All-terminal reliability Two-terminal reliability Failure type Graph theory |
| dc.title.none.fl_str_mv | Uniformly Optimally Reliable Graphs: A Survey |
| dc.type.es.fl_str_mv | Artículo |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/article |
| dc.type.version.es.fl_str_mv | Enviado |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/submittedVersion |
| description | Which is the most reliable graph with n nodes and m edges? This celebrated problem has several aspects, according to the notion of optimality (in a local or uniform sense), failure type (either nodes or edges), or reliability model (all-terminal connectedness, two-terminal or multiterminal setting). This article presents a chronological survey of the multiple proposals to address the problem, together with recent trends and enigmatic conjectures posed decades ago that promote further research. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | REDI_ea324a95b9b36194ec7c59e8eec86bec |
| identifier_str_mv | FCE_1_2019_1_156693 10.1002/net.22085 |
| instacron_str | Agencia Nacional de Investigación e Innovación |
| institution | Agencia Nacional de Investigación e Innovación |
| instname_str | Agencia Nacional de Investigación e Innovación |
| language | eng |
| network_acronym_str | REDI |
| network_name_str | REDI |
| oai_identifier_str | oai:redi.anii.org.uy:20.500.12381/699 |
| publishDate | 2021 |
| reponame_str | REDI |
| repository.mail.fl_str_mv | jmaldini@anii.org.uy |
| repository.name.fl_str_mv | REDI - Agencia Nacional de Investigación e Innovación |
| repository_id_str | 9421 |
| rights_invalid_str_mv | Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional. (CC BY-NC-ND) Acceso abierto 2022-12-06 |
| spelling | Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional. (CC BY-NC-ND)Acceso abierto2022-12-06info:eu-repo/semantics/openAccess2022-10-20T23:26:20Z2021-12-06https://hdl.handle.net/20.500.12381/699FCE_1_2019_1_15669310.1002/net.22085Which is the most reliable graph with n nodes and m edges? This celebrated problem has several aspects, according to the notion of optimality (in a local or uniform sense), failure type (either nodes or edges), or reliability model (all-terminal connectedness, two-terminal or multiterminal setting). This article presents a chronological survey of the multiple proposals to address the problem, together with recent trends and enigmatic conjectures posed decades ago that promote further research.Agencia Nacional de Investigación e InnovaciónengWileyNetworksreponame:REDIinstname:Agencia Nacional de Investigación e Innovacióninstacron:Agencia Nacional de Investigación e InnovaciónUniformly most reliable graphUniformly least reliable graphAll-terminal reliabilityTwo-terminal reliabilityFailure typeGraph theoryCiencias Naturales y ExactasMatemáticasMatemática AplicadaUniformly Optimally Reliable Graphs: A SurveyArtículoEnviadoinfo:eu-repo/semantics/submittedVersioninfo:eu-repo/semantics/articleUniversidad de la RepúblicaUniversidad de Buenos Aires//Ciencias Naturales y Exactas/Matemáticas/Matemática AplicadaRomero, PabloLICENSElicense.txtlicense.txttext/plain; charset=utf-84944https://redi.anii.org.uy/jspui/bitstream/20.500.12381/699/2/license.txt3c9d86d36485746409b4281a0893d729MD52ORIGINAL1 (1).pdf1 (1).pdfSurveyapplication/pdf309737https://redi.anii.org.uy/jspui/bitstream/20.500.12381/699/1/1%20%281%29.pdf0cd7d61180725b15d5ee832302829f37MD5120.500.12381/6992023-06-13 13:55:00.965oai:redi.anii.org.uy:20.500.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- Agencia Nacional de Investigación e Innovaciónfalse |
| spellingShingle | Uniformly Optimally Reliable Graphs: A Survey Romero, Pablo Uniformly most reliable graph Uniformly least reliable graph All-terminal reliability Two-terminal reliability Failure type Graph theory Ciencias Naturales y Exactas Matemáticas Matemática Aplicada |
| status_str | submittedVersion |
| title | Uniformly Optimally Reliable Graphs: A Survey |
| title_full | Uniformly Optimally Reliable Graphs: A Survey |
| title_fullStr | Uniformly Optimally Reliable Graphs: A Survey |
| title_full_unstemmed | Uniformly Optimally Reliable Graphs: A Survey |
| title_short | Uniformly Optimally Reliable Graphs: A Survey |
| title_sort | Uniformly Optimally Reliable Graphs: A Survey |
| topic | Uniformly most reliable graph Uniformly least reliable graph All-terminal reliability Two-terminal reliability Failure type Graph theory Ciencias Naturales y Exactas Matemáticas Matemática Aplicada |
| url | https://hdl.handle.net/20.500.12381/699 |
