{"id":190138,"date":"2013-11-19T00:00:00","date_gmt":"2013-11-22T15:10:27","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/hardness-of-robust-graph-isomorphism-lasserre-gaps-and-asymmetry-of-random-graphs\/"},"modified":"2016-08-02T06:12:38","modified_gmt":"2016-08-02T13:12:38","slug":"hardness-of-robust-graph-isomorphism-lasserre-gaps-and-asymmetry-of-random-graphs","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/hardness-of-robust-graph-isomorphism-lasserre-gaps-and-asymmetry-of-random-graphs\/","title":{"rendered":"Hardness of Robust Graph Isomorphism, Lasserre Gaps, and Asymmetry of Random Graphs"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Given two graphs which are almost isomorphic, is it possible to find a bijection which preserves most of the edges between the two?  This is the algorithmic task of Robust Graph Isomorphism, which is a natural approximation variation of the Graph Isomorphism problem.  In this talk, we show that no polynomial-time algorithm solves this problem, conditioned on Feige&#8217;s Random 3XOR Hypothesis.  In addition, we show that the Lasserre\/SOS SDP hierarchy, the most powerful SDP hierarchy known, fails quite spectacularly on this problem: it needs a linear number of rounds to distinguish two isomorphic graphs from two far-from-isomorphic graphs.  Along the way, we venture into the theory of random graphs by showing that a random graph is robustly asymmetric whp, meaning that any permutation which is close to an automorphism is itself close to the identity permutation.<\/p>\n<p>Joint work with Ryan O&#8217;Donnell, John Wright, and Chenggang Wu.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Given two graphs which are almost isomorphic, is it possible to find a bijection which preserves most of the edges between the two? This is the algorithmic task of Robust Graph Isomorphism, which is a natural approximation variation of the Graph Isomorphism problem. In this talk, we show that no polynomial-time algorithm solves this problem, [&hellip;]<\/p>\n","protected":false},"featured_media":197989,"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":[206954],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-190138","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-video-type-microsoft-research-talks","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/gAsQsEMgWU0","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/190138","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\/190138\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/197989"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=190138"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=190138"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=190138"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=190138"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=190138"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=190138"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=190138"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=190138"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=190138"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=190138"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}