{"id":13281,"date":"2021-12-08T21:00:40","date_gmt":"2021-12-09T02:00:40","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=13281"},"modified":"2026-06-02T14:59:23","modified_gmt":"2026-06-02T18:59:23","slug":"tr-08-19-communication-efficient-construction-of-the-plane-localized-delaunay-graph","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-2008\/tr-08-19-communication-efficient-construction-of-the-plane-localized-delaunay-graph\/","title":{"rendered":"TR-08-19: Communication-Efficient Construction of the Plane Localized Delaunay Graph"},"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-08-19: Communication-Efficient Construction of the Plane Localized Delaunay Graph\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-2008\/\">Technical Report<\/a> TR-08-19<br>\nSeptember 17, 2008<\/p>\n\n\n\n<h2 id=\"communication-efficient-construction-of-the-plane-localized-delaunay-graph\" class=\"wp-block-heading\">Communication-Efficient Construction of the Plane Localized Delaunay Graph<\/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<p class=\"tr_t3\">P Bose, P Carmi, M Smid, D Xu<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div>\n<h3>Abstract<\/h3>\n<p>Let V be a finite set of points in the plane. We present a 2-local algorithm that constructs a plane 4pi(sqrt3)\/9-spanner of the unit-disk graph UDG(V ). This algorithm makes only one round of communication and each point of V broadcasts at most 5 messages. This improves the previously best message-bound of 11 by Araujo and Rodrigues (Fast localized Delaunay triangulation, Lecture Notes in Computer Science, volume 3544,2004).<\/p>\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/TR-08-19-Carmi.pdf\">TR-08-19.pdf<\/a><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Carleton University Technical Report TR-08-19 September 17, 2008 Communication-Efficient Construction of the Plane Localized Delaunay Graph P Bose, P Carmi, M Smid, D Xu Abstract Let V be a finite set of points in the plane. We present a 2-local algorithm that constructs a plane 4pi(sqrt3)\/9-spanner of the unit-disk graph UDG(V ). This algorithm makes [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":12410,"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-13281","page","type-page","status-publish","hentry"],"acf":{"cu_post_thumbnail":false},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/13281","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=13281"}],"version-history":[{"count":1,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/13281\/revisions"}],"predecessor-version":[{"id":13282,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/13281\/revisions\/13282"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12410"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=13281"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=13281"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}