{"id":191853,"date":"2014-12-08T00:00:00","date_gmt":"2015-02-04T14:49:52","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/tutorial-recent-progress-in-the-structure-of-large-treewidth-graphs-and-some-applications\/"},"modified":"2017-04-19T12:20:31","modified_gmt":"2017-04-19T19:20:31","slug":"tutorial-recent-progress-in-the-structure-of-large-treewidth-graphs-and-some-applications","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/tutorial-recent-progress-in-the-structure-of-large-treewidth-graphs-and-some-applications\/","title":{"rendered":"Tutorial: Recent Progress in the Structure of Large-Treewidth Graphs and Some Applications"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Tree decompositions and treewidth play a key role in the seminal work of Robertson and Seymour on graph minors. One of their fundamental results is the Excluded-Grid Theorem which states that every graph G with treewidth at least k contains a f(k) x f(k) grid-minor for some (slowly growing) function f. Treewidth-based ideas have, over the years, yielded many algorithmic and structural results on graphs and related structures.<\/p>\n<p>There have been some recent advances in our understanding of the structure of graphs with large treewidth. These advances were partly motivated by the study of polynomial-time approximation algorithms for the maximum disjoint paths problem, culminating in a breakthrough by Chuzhoy in 2011. Subsequent work, building upon some of her ideas and other tools, has led to several new results including a polynomial relationship between treewidth of a graph and the size of its largest grid-minor.<\/p>\n<p>The tutorial will provide relevant background on treewidth, describe the highlights of recent developments, and a few applications.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tree decompositions and treewidth play a key role in the seminal work of Robertson and Seymour on graph minors. One of their fundamental results is the Excluded-Grid Theorem which states that every graph G with treewidth at least k contains a f(k) x f(k) grid-minor for some (slowly growing) function f. Treewidth-based ideas have, over [&hellip;]<\/p>\n","protected":false},"featured_media":198826,"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-191853","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/2xw8JCA6qkk","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/191853","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\/191853\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/198826"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=191853"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=191853"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=191853"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=191853"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=191853"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=191853"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=191853"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=191853"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=191853"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=191853"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}