A PageRank Algorithm based on Asynchronous Gauss-Seidel Iterations
Autor(a) principal: | |
---|---|
Data de Publicação: | 2018 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/11144/3875 |
Resumo: | We address the PageRank problem of associating a relative importance value to all web pages in the Internet so that a search engine can use them to sort which pages to show to the user. This precludes finding the eigenvector associated with a particular eigenvalue of the link matrix constructed from the topology graph of the web. In this paper, we investigate the potential benefits of addressing the problem as a solution of a set of linear equations. Initial results suggest that using an asynchronous version of the Gauss-Seidel method can yield a faster convergence than using the traditional power method while maintaining the communications according to the sparse link matrix of the web and avoiding the strict sequential update of the Gauss-Seidel method. Such an alternative poses an interesting path for future research given the benefits of using other more advanced methods to solve systems of linear equations. Additionally, it is investigated the benefits of having a projection after all page ranks have been updated as to maintain all its entries summing to one and positive. In simulations, it is provided evidence to support future research on approximation rules that can be used to avoid the need for the projection to the $n$-simplex (the projection represents in some cases a threefold increase in the convergence rate over the power method) and on the loss in performance by using an asynchronous algorithm. |
id |
RCAP_a5dbcb8487ae51d9912124ddc6c9b6e6 |
---|---|
oai_identifier_str |
oai:repositorio.ual.pt:11144/3875 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
A PageRank Algorithm based on Asynchronous Gauss-Seidel Iterationseigenvalues and eigenfunctionsgraph theoryInternetiterative methodsmatrix algebrasearch enginestopologyasynchronous versionGauss-Seidel methodtraditional power methodsparse link matrixlinear equationspage ranksasynchronous algorithmPageRank algorithmasynchronous Gauss-Seidel iterationsPageRank problemrelative importance valueweb pagessearch enginetopology graphsequential updatelink matrix eigenvalueProgram processorsConvergenceMathematical modelEigenvalues and eigenfunctionsWeb pagesSearch enginesToolsWe address the PageRank problem of associating a relative importance value to all web pages in the Internet so that a search engine can use them to sort which pages to show to the user. This precludes finding the eigenvector associated with a particular eigenvalue of the link matrix constructed from the topology graph of the web. In this paper, we investigate the potential benefits of addressing the problem as a solution of a set of linear equations. Initial results suggest that using an asynchronous version of the Gauss-Seidel method can yield a faster convergence than using the traditional power method while maintaining the communications according to the sparse link matrix of the web and avoiding the strict sequential update of the Gauss-Seidel method. Such an alternative poses an interesting path for future research given the benefits of using other more advanced methods to solve systems of linear equations. Additionally, it is investigated the benefits of having a projection after all page ranks have been updated as to maintain all its entries summing to one and positive. In simulations, it is provided evidence to support future research on approximation rules that can be used to avoid the need for the projection to the $n$-simplex (the projection represents in some cases a threefold increase in the convergence rate over the power method) and on the loss in performance by using an asynchronous algorithm.IEEE2018-09-12T15:42:54Z2018-06-27T00:00:00Z2018-06-27info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/11144/3875eng978-1-5386-5428-62378-586110.23919/ACC.2018.8431212Silvestre, DanielHespanha, JoãoSilvestre, Carlosinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-01-11T02:08:51Zoai:repositorio.ual.pt:11144/3875Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:31:38.235694Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
A PageRank Algorithm based on Asynchronous Gauss-Seidel Iterations |
title |
A PageRank Algorithm based on Asynchronous Gauss-Seidel Iterations |
spellingShingle |
A PageRank Algorithm based on Asynchronous Gauss-Seidel Iterations Silvestre, Daniel eigenvalues and eigenfunctions graph theory Internet iterative methods matrix algebra search engines topology asynchronous version Gauss-Seidel method traditional power method sparse link matrix linear equations page ranks asynchronous algorithm PageRank algorithm asynchronous Gauss-Seidel iterations PageRank problem relative importance value web pages search engine topology graph sequential update link matrix eigenvalue Program processors Convergence Mathematical model Eigenvalues and eigenfunctions Web pages Search engines Tools |
title_short |
A PageRank Algorithm based on Asynchronous Gauss-Seidel Iterations |
title_full |
A PageRank Algorithm based on Asynchronous Gauss-Seidel Iterations |
title_fullStr |
A PageRank Algorithm based on Asynchronous Gauss-Seidel Iterations |
title_full_unstemmed |
A PageRank Algorithm based on Asynchronous Gauss-Seidel Iterations |
title_sort |
A PageRank Algorithm based on Asynchronous Gauss-Seidel Iterations |
author |
Silvestre, Daniel |
author_facet |
Silvestre, Daniel Hespanha, João Silvestre, Carlos |
author_role |
author |
author2 |
Hespanha, João Silvestre, Carlos |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Silvestre, Daniel Hespanha, João Silvestre, Carlos |
dc.subject.por.fl_str_mv |
eigenvalues and eigenfunctions graph theory Internet iterative methods matrix algebra search engines topology asynchronous version Gauss-Seidel method traditional power method sparse link matrix linear equations page ranks asynchronous algorithm PageRank algorithm asynchronous Gauss-Seidel iterations PageRank problem relative importance value web pages search engine topology graph sequential update link matrix eigenvalue Program processors Convergence Mathematical model Eigenvalues and eigenfunctions Web pages Search engines Tools |
topic |
eigenvalues and eigenfunctions graph theory Internet iterative methods matrix algebra search engines topology asynchronous version Gauss-Seidel method traditional power method sparse link matrix linear equations page ranks asynchronous algorithm PageRank algorithm asynchronous Gauss-Seidel iterations PageRank problem relative importance value web pages search engine topology graph sequential update link matrix eigenvalue Program processors Convergence Mathematical model Eigenvalues and eigenfunctions Web pages Search engines Tools |
description |
We address the PageRank problem of associating a relative importance value to all web pages in the Internet so that a search engine can use them to sort which pages to show to the user. This precludes finding the eigenvector associated with a particular eigenvalue of the link matrix constructed from the topology graph of the web. In this paper, we investigate the potential benefits of addressing the problem as a solution of a set of linear equations. Initial results suggest that using an asynchronous version of the Gauss-Seidel method can yield a faster convergence than using the traditional power method while maintaining the communications according to the sparse link matrix of the web and avoiding the strict sequential update of the Gauss-Seidel method. Such an alternative poses an interesting path for future research given the benefits of using other more advanced methods to solve systems of linear equations. Additionally, it is investigated the benefits of having a projection after all page ranks have been updated as to maintain all its entries summing to one and positive. In simulations, it is provided evidence to support future research on approximation rules that can be used to avoid the need for the projection to the $n$-simplex (the projection represents in some cases a threefold increase in the convergence rate over the power method) and on the loss in performance by using an asynchronous algorithm. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018-09-12T15:42:54Z 2018-06-27T00:00:00Z 2018-06-27 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/11144/3875 |
url |
http://hdl.handle.net/11144/3875 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
978-1-5386-5428-6 2378-5861 10.23919/ACC.2018.8431212 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
IEEE |
publisher.none.fl_str_mv |
IEEE |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
|
_version_ |
1799136797951787008 |