{"version":"1.0","provider_name":"Microsoft Research","provider_url":"https:\/\/www.microsoft.com\/en-us\/research","author_name":"Tricia Mayer","author_url":"https:\/\/www.microsoft.com\/en-us\/research\/people\/tmayer\/","title":"How to Complete a Doubling Metric - Microsoft Research","type":"rich","width":600,"height":338,"html":"<blockquote class=\"wp-embedded-content\" data-secret=\"rfeujTCA3i\"><a href=\"https:\/\/www.microsoft.com\/en-us\/research\/publication\/how-to-complete-a-doubling-metric\/\">How to Complete a Doubling Metric<\/a><\/blockquote><iframe sandbox=\"allow-scripts\" security=\"restricted\" src=\"https:\/\/www.microsoft.com\/en-us\/research\/publication\/how-to-complete-a-doubling-metric\/embed\/#?secret=rfeujTCA3i\" width=\"600\" height=\"338\" title=\"&#8220;How to Complete a Doubling Metric&#8221; &#8212; Microsoft Research\" data-secret=\"rfeujTCA3i\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\" class=\"wp-embedded-content\"><\/iframe><script type=\"text\/javascript\">\n\/* <![CDATA[ *\/\n\/*! This file is auto-generated *\/\n!function(d,l){\"use strict\";l.querySelector&&d.addEventListener&&\"undefined\"!=typeof URL&&(d.wp=d.wp||{},d.wp.receiveEmbedMessage||(d.wp.receiveEmbedMessage=function(e){var t=e.data;if((t||t.secret||t.message||t.value)&&!\/[^a-zA-Z0-9]\/.test(t.secret)){for(var s,r,n,a=l.querySelectorAll('iframe[data-secret=\"'+t.secret+'\"]'),o=l.querySelectorAll('blockquote[data-secret=\"'+t.secret+'\"]'),c=new RegExp(\"^https?:$\",\"i\"),i=0;i<o.length;i++)o[i].style.display=\"none\";for(i=0;i<a.length;i++)s=a[i],e.source===s.contentWindow&&(s.removeAttribute(\"style\"),\"height\"===t.message?(1e3<(r=parseInt(t.value,10))?r=1e3:~~r<200&&(r=200),s.height=r):\"link\"===t.message&&(r=new URL(s.getAttribute(\"src\")),n=new URL(t.value),c.test(n.protocol))&&n.host===r.host&&l.activeElement===s&&(d.top.location.href=t.value))}},d.addEventListener(\"message\",d.wp.receiveEmbedMessage,!1),l.addEventListener(\"DOMContentLoaded\",function(){for(var e,t,s=l.querySelectorAll(\"iframe.wp-embedded-content\"),r=0;r<s.length;r++)(t=(e=s[r]).getAttribute(\"data-secret\"))||(t=Math.random().toString(36).substring(2,12),e.src+=\"#?secret=\"+t,e.setAttribute(\"data-secret\",t)),e.contentWindow.postMessage({message:\"ready\",secret:t},\"*\")},!1)))}(window,document);\n\/\/# sourceURL=https:\/\/www.microsoft.com\/en-us\/research\/wp-includes\/js\/wp-embed.min.js\n\/* ]]> *\/\n<\/script>\n","description":"In recent years, considerable advances have been made in the study of properties of metric spaces in terms of their doubling dimension. This line of research has not only enhanced our understanding of finite metrics, but has also resulted in many algorithmic applications. However, we still do not understand the interaction between various graph-theoretic (topological) [&hellip;]"}