{"id":182696,"date":"2008-01-28T00:00:00","date_gmt":"2009-10-31T09:55:06","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/candidate-talk-query-lower-bounds-for-matroids-via-group-representations\/"},"modified":"2016-09-09T09:58:45","modified_gmt":"2016-09-09T16:58:45","slug":"candidate-talk-query-lower-bounds-for-matroids-via-group-representations","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/candidate-talk-query-lower-bounds-for-matroids-via-group-representations\/","title":{"rendered":"Candidate Talk: Query Lower Bounds for Matroids via Group Representations"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Finding an common independent set in two matroids is one of<br \/>\nthe classical problems of combinatorial optimization, including<br \/>\nthe well-known bipartite matching problem as a special case.<br \/>\nIn the early 1970s, algorithms for this problem were discovered<br \/>\nthat use O(n<sup>3<\/sup>) queries for matroids on n elements. In Welsh&#8217;s<br \/>\n1976 text on matroid theory, he asked the question of whether<br \/>\nthese algorithms are optimal.  In the following thirty years,<br \/>\nno non-trivial lower bounds were found.<\/p>\n<p>In this talk, I will present the first lower bound for this problem.<br \/>\nWe show that (log<sub>2<\/sub> 3)*n queries are necessary for certain matroids.<br \/>\nThe arguments are based on communication complexity and representation<br \/>\ntheory of the symmetric group.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Finding an common independent set in two matroids is one of the classical problems of combinatorial optimization, including the well-known bipartite matching problem as a special case. In the early 1970s, algorithms for this problem were discovered that use O(n3) queries for matroids on n elements. In Welsh&#8217;s 1976 text on matroid theory, he asked [&hellip;]<\/p>\n","protected":false},"featured_media":194735,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr_hide_image_in_river":0,"footnotes":""},"research-area":[],"msr-video-type":[],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-182696","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/tp1tWgzMLMs","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/182696","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/182696\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/194735"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=182696"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=182696"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=182696"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=182696"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=182696"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=182696"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=182696"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=182696"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=182696"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=182696"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}