{"id":15111,"date":"2022-06-18T19:26:34","date_gmt":"2022-06-18T23:26:34","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=15111"},"modified":"2026-06-08T14:54:35","modified_gmt":"2026-06-08T18:54:35","slug":"tr-231-optimal-elections-in-labeled-hypercubes","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1993\/tr-231-optimal-elections-in-labeled-hypercubes\/","title":{"rendered":"TR-231: Optimal Elections in Labeled Hypercubes"},"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-231: Optimal Elections in Labeled Hypercubes\n                    <\/h1>\n                \n                                \n                            <\/header>\n\n                    <\/div>\n\n            <\/div>\n\n    <\/div>\n<\/section>\n\n\n\n<p>Carleton University<br><a href=\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1993\/\">Technical Report<\/a>&nbsp;<strong>TR-231<\/strong><br>December 1993<\/p>\n\n\n\n<h2 id=\"optimal-elections-in-labeled-hypercubes\" class=\"wp-block-heading\">Optimal Elections in Labeled Hypercubes<\/h2>\n\n\n\n<p>Paola Flocchini &amp; Bernard Mans<\/p>\n\n\n\n<h3 id=\"abstract\" class=\"wp-block-heading\">Abstract<\/h3>\n\n\n\n<p>We study the message complexity of the Election problem in Hypercube net\u00adworks, when the processors have a \u201cSense of Direction\u201d, i.e. the capability to distinguish between adjacent communication links according to some globally con\u00adsistent scheme.<br>We present an original 0(N) messages algorithm which uses the natural dimen\u00adsional labeling of the communication links; to date, the best existing bound was O(N log N) messages. This result answers a long-standing open problem posed by the 0(N) messages bound for chordal rings [1].<br>We also consider the Election problem for Hypercube with another common labeling which is distance-based. We prove that, in this case the problem becomes drastically simplified and we present a 0(N) messages solution. Finally, we study the communication cost to change one orientation labeling to the other and prove that O(N) messages suffice.<\/p>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/TR-231.pdf\">TR-231.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton UniversityTechnical Report&nbsp;TR-231December 1993 Optimal Elections in Labeled Hypercubes Paola Flocchini &amp; Bernard Mans Abstract We study the message complexity of the Election problem in Hypercube net\u00adworks, when the processors have a \u201cSense of Direction\u201d, i.e. the capability to distinguish between adjacent communication links according to some globally con\u00adsistent scheme.We present an original 0(N) messages [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":11912,"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-15111","page","type-page","status-publish","hentry"],"acf":{"cu_post_thumbnail":""},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/15111","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=15111"}],"version-history":[{"count":2,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/15111\/revisions"}],"predecessor-version":[{"id":24442,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/15111\/revisions\/24442"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/11912"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=15111"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=15111"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}