{"id":157932,"date":"2008-07-18T00:00:00","date_gmt":"2008-07-18T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/statistical-mechanics-of-steiner-trees\/"},"modified":"2018-10-16T20:59:26","modified_gmt":"2018-10-17T03:59:26","slug":"statistical-mechanics-of-steiner-trees","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/statistical-mechanics-of-steiner-trees\/","title":{"rendered":"Statistical Mechanics of Steiner Trees"},"content":{"rendered":"<div class=\"asset-content\">\n<p>The minimum weight Steiner tree (MST) is an important combinatorial optimization problem over networks that has applications in a wide range of fields. Here we discuss a general technique to translate the imposed global connectivity constrain into many local ones that can be analyzed with cavity equation techniques. This approach leads to a new ptimization algorithm for MST and allows us to analyze the statistical mechanics properties of MST on random graphs of various types.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The minimum weight Steiner tree (MST) is an important combinatorial optimization problem over networks that has applications in a wide range of fields. Here we discuss a general technique to translate the imposed global connectivity constrain into many local ones that can be analyzed with cavity equation techniques. This approach leads to a new ptimization [&hellip;]<\/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":[13561],"msr-publication-type":[193715],"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-157932","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-locale-en_us"],"msr_publishername":"","msr_edition":"Physical Review Letters","msr_affiliation":"","msr_published_date":"2008-07-18","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"","msr_chapter":"","msr_isbn":"","msr_journal":"Physical Review Letters","msr_volume":"","msr_number":"MSR-TR-2008-188","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":"208137","msr_publicationurl":"","msr_doi":"10.1103\/PhysRevLett.101.037208","msr_publication_uploader":[{"type":"file","title":"1-Steiner-PRL.pdf","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/02\/1-Steiner-PRL.pdf","id":208137,"label_id":0},{"type":"doi","title":"10.1103\/PhysRevLett.101.037208","viewUrl":false,"id":false,"label_id":0}],"msr_related_uploader":"","msr_attachments":[{"id":208137,"url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/02\/1-Steiner-PRL.pdf"}],"msr-author-ordering":[{"type":"text","value":"M. Bayati","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":"text","value":"A. Braunstein","user_id":0,"rest_url":false},{"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":"A. Ramezanpour","user_id":0,"rest_url":false},{"type":"text","value":"R. 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