{"id":13132,"date":"2021-12-06T18:53:37","date_gmt":"2021-12-06T23:53:37","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=13132"},"modified":"2026-06-02T14:59:24","modified_gmt":"2026-06-02T18:59:24","slug":"tr-05-03-a-new-approach-for-solving-the-maximum-clique-problem-2","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-2005\/tr-05-03-a-new-approach-for-solving-the-maximum-clique-problem-2\/","title":{"rendered":"TR-05-03: A New Approach for Solving the Maximum Clique Problem"},"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-05-03: A New Approach for Solving the Maximum Clique Problem\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-2005\/\">Technical Report<\/a> TR-05-03<br>\nApril 15, 2005<\/p>\n\n\n\n<h2 id=\"a-new-approach-for-solving-the-maximum-clique-problem\" class=\"wp-block-heading\">A New Approach for Solving the Maximum Clique Problem<\/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\">\n<div class=\"tr_t3\">Peter J. Taillon<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div>\n<h3>Abstract<\/h3>\n<p>In this report, we describe an improved exact algorithm for solving the Maximum Clique problem in a graph using a novel sampling technique combined with the FPT k-vertex cover algorithm. We also introduce a very effective heuristic for finding a maximum clique that combines our sampling approach with fast independent set approximation. Experimental research indicates that this approach matches or outperforms the current best algorithms for finding a maximum clique in a graph, with significantly smaller runtimes.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/TR-05-03.pdf\">TR-05-03.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton University Technical Report TR-05-03 April 15, 2005 A New Approach for Solving the Maximum Clique Problem Peter J. Taillon Abstract In this report, we describe an improved exact algorithm for solving the Maximum Clique problem in a graph using a novel sampling technique combined with the FPT k-vertex cover algorithm. We also introduce a [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":12337,"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-13132","page","type-page","status-publish","hentry"],"acf":{"cu_post_thumbnail":false},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/13132","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=13132"}],"version-history":[{"count":2,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/13132\/revisions"}],"predecessor-version":[{"id":13135,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/13132\/revisions\/13135"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12337"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=13132"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=13132"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}