{"id":184621,"date":"2010-01-21T00:00:00","date_gmt":"2010-01-25T08:07:20","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/understanding-the-limitations-of-linear-and-semidefinite-programming\/"},"modified":"2016-08-22T11:27:59","modified_gmt":"2016-08-22T18:27:59","slug":"understanding-the-limitations-of-linear-and-semidefinite-programming","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/understanding-the-limitations-of-linear-and-semidefinite-programming\/","title":{"rendered":"Understanding the Limitations of Linear and Semidefinite Programming"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Linear and Semidefinite programs provide the best approximation algorithms for many NP-hard combinatorial optimization problems.  This talk will introduce recent techniques to give unconditional lower bounds for algorithms based on Linear and Semidefinite programs (LPs and SDPs, respectively).  In particular, I will define and give background about LP and SDP hierarchies, which include a large class of SDPs and LPs including the most famous SDP algorithms (which occur very low in the hierarchy).  I will then sketch two lower bounds for these hierarchies.  The first result shows that a large class of linear programs (generated by the Lovasz-Schrijver hierarchy) requires exponential time to approximate Vertex Cover to better than a factor of 2-epsilon.  The second result shows that a large class of semidefinite programs (generated by the Lasserre hierarchy) requires exponential time to refute a random 3-XOR instance (even though such an instance is very far from satisfiable).  As a corollary, the same class requires exponential time to  approximate Vertex Cover to better than a factor of 7\/6-epsilon.  This result is the first construction of a Lasserre integrality gap, and simplifies, strengthens, and helps to explain several previous results.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Linear and Semidefinite programs provide the best approximation algorithms for many NP-hard combinatorial optimization problems. This talk will introduce recent techniques to give unconditional lower bounds for algorithms based on Linear and Semidefinite programs (LPs and SDPs, respectively). In particular, I will define and give background about LP and SDP hierarchies, which include a large [&hellip;]<\/p>\n","protected":false},"featured_media":195513,"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-184621","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/hiFq_kJ3xvg","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/184621","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\/184621\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/195513"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=184621"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=184621"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=184621"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=184621"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=184621"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=184621"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=184621"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=184621"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=184621"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=184621"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}