{"id":13054,"date":"2021-12-05T20:29:54","date_gmt":"2021-12-06T01:29:54","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=13054"},"modified":"2026-06-02T14:59:24","modified_gmt":"2026-06-02T18:59:24","slug":"tr-01-07-o-optimal-planar-embedding-using-graph-seperators","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-2001\/tr-01-07-o-optimal-planar-embedding-using-graph-seperators\/","title":{"rendered":"TR-01-07: O-Optimal Planar Embedding using Graph Seperators"},"content":{"rendered":"\n<section class=\"w-screen px-6 cu-section cu-section--white ml-offset-center md:px-8 lg:px-14\">\n    <div class=\"space-y-6 cu-max-w-child-5xl  md:space-y-10 cu-prose-first-last\">\n\n            <div class=\"cu-textmedia flex flex-col lg:flex-row mx-auto gap-6 md:gap-10 my-6 md:my-12 first:mt-0 max-w-5xl\">\n        <div class=\"justify-start cu-textmedia-content cu-prose-first-last\" style=\"flex: 0 0 100%;\">\n            <header class=\"font-light prose-xl cu-pageheader md:prose-2xl cu-component-updated cu-prose-first-last\">\n                                    <h1 class=\"cu-prose-first-last font-semibold !mt-2 mb-4 md:mb-6 relative after:absolute after:h-px after:bottom-0 after:bg-cu-red after:left-px text-3xl md:text-4xl lg:text-5xl lg:leading-[3.5rem] pb-5 after:w-10 text-cu-black-700 not-prose\">\n                        TR-01-07: O-Optimal Planar Embedding using Graph Seperators\n                    <\/h1>\n                \n                                \n                            <\/header>\n\n                    <\/div>\n\n            <\/div>\n\n    <\/div>\n<\/section>\n\n<p>Carleton University<br>\n<a href=\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-2001\/\">Technical Report<\/a> TR-01-07<br>\nJuly 2001<\/p>\n\n\n\n<h2 id=\"o-optimal-planar-embedding-using-graph-seperators\" class=\"wp-block-heading\">O-Optimal Planar Embedding using Graph Seperators<\/h2>\n\n\n\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">Norbert Zeh<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div>\n<h3>Abstract<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<p>We present a new algorithm to test whether a given graph G is planar and to compute a planar embedding \u02c6G of G if such an embedding exists. Our algorithmutilizes a fundamentally new approach based on graph separators to obtain such an embedding. The I\/O-complexity of our algorithm is O(sort(N)). A simple simulation technique reduces the I\/O-complexity of our algorithm to O(perm(N)). We prove a matching lower bound of W(perm(N)) I\/Os for computing a planar embedding of a given planar graph.<\/p>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/TR-01-07.pdf\">TR-01-07.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton University Technical Report TR-01-07 July 2001 O-Optimal Planar Embedding using Graph Seperators Norbert Zeh Abstract We present a new algorithm to test whether a given graph G is planar and to compute a planar embedding \u02c6G of G if such an embedding exists. Our algorithmutilizes a fundamentally new approach based on graph separators to [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":12272,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"_cu_dining_location_slug":"","footnotes":"","_links_to":"","_links_to_target":""},"cu_page_type":[],"class_list":["post-13054","page","type-page","status-publish","hentry"],"acf":{"cu_post_thumbnail":false},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/13054","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/comments?post=13054"}],"version-history":[{"count":1,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/13054\/revisions"}],"predecessor-version":[{"id":13055,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/13054\/revisions\/13055"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12272"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=13054"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=13054"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}