{"id":357926,"date":"2017-01-25T14:35:55","date_gmt":"2017-01-25T22:35:55","guid":{"rendered":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/?post_type=msr-research-item&p=357926"},"modified":"2018-10-16T21:00:50","modified_gmt":"2018-10-17T04:00:50","slug":"pairs-shortest-paths-on2-time-high-probability","status":"publish","type":"msr-research-item","link":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/publication\/pairs-shortest-paths-on2-time-high-probability\/","title":{"rendered":"All-Pairs Shortest Paths In O(n^2) Time With High Probability"},"content":{"rendered":"

We present an all-pairs shortest path algorithm whose running time on a complete directed graph on n<\/span><\/span><\/span><\/span> vertices whose edge weights are chosen independently and uniformly at random from [<\/span>0<\/span>,<\/span>1<\/span>]<\/span><\/span><\/span><\/span> is O<\/span>(<\/span>n<\/span>2<\/span><\/span>)<\/span><\/span><\/span><\/span>, in expectation and with high probability. This resolves a long standing open problem. The algorithm is a variant of the dynamic all-pairs shortest paths algorithm of Demetrescu and Italiano. The analysis relies on a proof that the number of \\emph{locally shortest paths} in such randomly weighted graphs is O<\/span>(<\/span>n<\/span>2<\/span><\/span>)<\/span><\/span><\/span><\/span>, in expectation and with high probability. We also present a dynamic version of the algorithm that recomputes all shortest paths after a random edge update in O<\/span>(<\/span>log<\/span>2<\/span><\/span><\/span><\/span><\/span>n<\/span>)<\/span><\/span><\/span><\/span> expected time.<\/p>\n","protected":false},"excerpt":{"rendered":"

We present an all-pairs shortest path algorithm whose running time on a complete directed graph on n vertices whose edge weights are chosen independently and uniformly at random from [0,1] is O(n2), in expectation and with high probability. This resolves a long standing open problem. The algorithm is a variant of the dynamic all-pairs shortest […]<\/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":"","msr-author-ordering":null,"msr_publishername":"IEEE","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"All-pairs shortest paths in O(n^2) time with high probability","msr_editors":"","msr_how_published":"","msr_isbn":"978-1-4244-8525-3","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"All-pairs shortest paths in O(n^2) time with high probability","msr_doi":"10.1109\/FOCS.2010.69","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"","msr_other_contributors":"","msr_speaker":"","msr_award":"","msr_affiliation":"","msr_institution":"","msr_host":"","msr_version":"","msr_duration":"","msr_original_fields_of_study":"","msr_release_tracker_id":"","msr_s2_match_type":"","msr_citation_count_updated":"","msr_published_date":"2010-10-26","msr_highlight_text":"","msr_notes":"","msr_longbiography":"","msr_publicationurl":"http:\/\/ieeexplore.ieee.org\/document\/5671327\/","msr_external_url":"","msr_secondary_video_url":"","msr_conference_url":"","msr_journal_url":"","msr_s2_pdf_url":"","msr_year":0,"msr_citation_count":0,"msr_influential_citations":0,"msr_reference_count":0,"msr_s2_match_confidence":0,"msr_microsoftintellectualproperty":true,"msr_s2_open_access":false,"msr_s2_author_ids":[],"msr_pub_ids":[],"msr_hide_image_in_river":0,"footnotes":""},"msr-research-highlight":[],"research-area":[13546],"msr-publication-type":[193716],"msr-publisher":[],"msr-focus-area":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-357926","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-computational-sciences-mathematics","msr-locale-en_us"],"msr_publishername":"IEEE","msr_edition":"All-pairs shortest paths in O(n^2) time with high probability","msr_affiliation":"","msr_published_date":"2010-10-26","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"","msr_chapter":"","msr_isbn":"978-1-4244-8525-3","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":"357929","msr_publicationurl":"http:\/\/ieeexplore.ieee.org\/document\/5671327\/","msr_doi":"10.1109\/FOCS.2010.69","msr_publication_uploader":[{"type":"file","title":"1105.3770v1","viewUrl":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-content\/uploads\/2017\/01\/1105.3770v1.pdf","id":357929,"label_id":0},{"type":"url","title":"http:\/\/ieeexplore.ieee.org\/document\/5671327\/","viewUrl":false,"id":false,"label_id":0},{"type":"doi","title":"10.1109\/FOCS.2010.69","viewUrl":false,"id":false,"label_id":0}],"msr_related_uploader":"","msr_citation_count":0,"msr_citation_count_updated":"","msr_s2_paper_id":"","msr_influential_citations":0,"msr_reference_count":0,"msr_arxiv_id":"","msr_s2_author_ids":[],"msr_s2_open_access":false,"msr_s2_pdf_url":null,"msr_attachments":[{"id":0,"url":"http:\/\/ieeexplore.ieee.org\/document\/5671327\/"}],"msr-author-ordering":[{"type":"user_nicename","value":"peres","user_id":33234,"rest_url":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=peres"},{"type":"text","value":"Dimitry Sotnikov","user_id":0,"rest_url":false},{"type":"text","value":"Benny Sudakov","user_id":0,"rest_url":false},{"type":"text","value":"Uri Zwick","user_id":0,"rest_url":false}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[],"msr_group":[],"msr_project":[],"publication":[],"video":[],"msr-tool":[],"msr_publication_type":"inproceedings","related_content":[],"_links":{"self":[{"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/357926","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item"}],"about":[{"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-research-item"}],"version-history":[{"count":2,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/357926\/revisions"}],"predecessor-version":[{"id":416807,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/357926\/revisions\/416807"}],"wp:attachment":[{"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/media?parent=357926"}],"wp:term":[{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=357926"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=357926"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=357926"},{"taxonomy":"msr-publisher","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-publisher?post=357926"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=357926"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=357926"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=357926"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=357926"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=357926"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=357926"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=357926"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=357926"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}