Motivated by the problem of detecting link-spam, we consider the following graph-theoretic primitive: Given a webgraph G, a vertex v in G, and a parameter \u03b4 \u2208 (0, 1), compute the set of all vertices that contribute to v at least a \u03b4 fraction of v\u2019s PageRank. We call this set the \u03b4-contributing set of v. To this end, we define the contribution vector of v to be the vector whose entries measure the contributions of every vertex to the PageRank of v. A local algorithm is one that produces a solution by adaptively examining only a small portion of the input graph near a specified vertex. We give an efficient local algorithm that computes an \u0003-approximation of the contribution vector for a given vertex by adaptively examining O(1\/\u0003) vertices. Using this algorithm, we give a local approximation algorithm for the primitive defined above. Specifically, we give an algorithm that returns a set containing the \u03b4-contributing set of v and at most O(1\/\u03b4) vertices from the \u03b4\/2-contributing set of v, and which does so by examining at most O(1\/\u03b4) vertices. We also give a local algorithm for solving the following problem: If there exist k vertices that contribute a \u03c1-fraction to the PageRank of v, find a set of k vertices that contribute at least a (\u03c1 \u2212 \u0003)-fraction to the PageRank of v. In this case, we prove that our algorithm examines at most O(k\/\u0003) vertices.<\/p>\n","protected":false},"excerpt":{"rendered":"
Motivated by the problem of detecting link-spam, we consider the following graph-theoretic primitive: Given a webgraph G, a vertex v in G, and a parameter \u03b4 \u2208 (0, 1), compute the set of all vertices that contribute to v at least a \u03b4 fraction of v\u2019s PageRank. We call this set the \u03b4-contributing set of […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13546],"msr-publication-type":[193716],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-316976","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-computational-sciences-mathematics","msr-locale-en_us"],"msr_publishername":"","msr_edition":"Proceedings of the 5th Workshop on Algorithms and Models for the Web Graph (WAW)","msr_affiliation":"","msr_published_date":"2007-01-01","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"150-165","msr_chapter":"","msr_isbn":"","msr_journal":"","msr_volume":"","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"","msr_organization":"","msr_how_published":"","msr_notes":"","msr_highlight_text":"","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":1,"msr_main_download":"459498","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"file","title":"local-computation-of-pagerank-contributions","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/uploads\/prod\/2016\/11\/Local-Computation-of-PageRank-Contributions.pdf","id":459498,"label_id":0}],"msr_related_uploader":"","msr_attachments":[],"msr-author-ordering":[{"type":"text","value":"Reid Andersen","user_id":0,"rest_url":false},{"type":"user_nicename","value":"borgs","user_id":31278,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=borgs"},{"type":"user_nicename","value":"jchayes","user_id":32200,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=jchayes"},{"type":"text","value":"John Hopcraft","user_id":0,"rest_url":false},{"type":"text","value":"Vahab S. 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