{"id":186301,"date":"2011-05-25T00:00:00","date_gmt":"2011-05-26T12:39:26","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/fast-averaging-and-applications-to-mapreduce-and-consensus-on-graphs\/"},"modified":"2016-08-22T11:31:40","modified_gmt":"2016-08-22T18:31:40","slug":"fast-averaging-and-applications-to-mapreduce-and-consensus-on-graphs","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/fast-averaging-and-applications-to-mapreduce-and-consensus-on-graphs\/","title":{"rendered":"Fast Averaging, and Applications to MapReduce and Consensus on Graphs"},"content":{"rendered":"<div class=\"asset-content\">\n<p>We look at the problem of computing the average (arithmetic mean) of a long vector of n numbers. Mathematically, this problem is simple; requires n &#8211; 1 additions and 1 division. However, some saving in the number of computations is possible if the vector exhibits certain regularity. In the extreme case, if all the numbers in the vector are equal to 5 (say), then we can get the exact answer with O(1) computations.<\/p>\n<p>This simple problem of finding the arithmetic mean is interesting in many applications, one of them being MapReduce-type computations. MapReduce is an architecture patented by Google, and is de facto standard for large-scale computations in today&#8217;s data centers. In this talk, we present a mathematical abstraction of MapReduce, and investigate it from the following points of view:<\/p>\n<ol>\n<li>Can we use a randomized algorithm to provide probabilistic performance guarantees, while speeding-up the overall completion time of a query?<\/li>\n<li>What is the effect of &#8220;regularity&#8221; of the underlying vector on the query completion times?<\/li>\n<\/ol>\n<p>This idea of approximate mean computation &#8211; that is, gaining speed-up while settling for probabilistic performance guarantees &#8211; finds applications in a number of other fields including control, robotics, estimation, and so on. We will discuss its applications to consensus on graphs.<\/p>\n<p>Joint work with Devavrat Shah.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We look at the problem of computing the average (arithmetic mean) of a long vector of n numbers. Mathematically, this problem is simple; requires n &#8211; 1 additions and 1 division. However, some saving in the number of computations is possible if the vector exhibits certain regularity. In the extreme case, if all the numbers [&hellip;]<\/p>\n","protected":false},"featured_media":196167,"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-186301","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/O_vdYQAn2xQ","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/186301","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\/186301\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/196167"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=186301"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=186301"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=186301"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=186301"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=186301"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=186301"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=186301"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=186301"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=186301"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=186301"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}