{"id":12629,"date":"2021-11-14T20:20:03","date_gmt":"2021-11-15T01:20:03","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=12629"},"modified":"2026-06-02T14:59:26","modified_gmt":"2026-06-02T18:59:26","slug":"tr-121-n-o-n-algorithm-for-the-ecdf-searching-problem-for-arbitrary-dimensions-on-a-mesh-of-processors","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1987\/tr-121-n-o-n-algorithm-for-the-ecdf-searching-problem-for-arbitrary-dimensions-on-a-mesh-of-processors\/","title":{"rendered":"TR-121: n O(\u221an) Algorithm for the ECDF Searching Problem for Arbitrary Dimensions on a Mesh-of-Processors"},"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-121: n O(\u221an) Algorithm for the ECDF Searching Problem for Arbitrary Dimensions on a Mesh-of-Processors\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-1987\/\">Technical Report<\/a> <strong>TR-121<\/strong><br>\nOctober 1987<\/p>\n\n\n\n<h2 id=\"n-o%e2%88%9an-algorithm-for-the-ecdf-searching-problem-for-arbitrary-dimensions-on-a-mesh-of-processors\" class=\"wp-block-heading tr_t1\">n O(\u221an) Algorithm for the ECDF Searching Problem for Arbitrary Dimensions on a Mesh-of-Processors<\/h2>\n\n\n\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">Frank Dehne &amp; Ivan Stojmenovic<\/div>\n<\/div>\n\n\n\n<div>\n<h3>Abstract<\/h3>\n<p>[1] presented an optimal O(&#8216;Jn} time parallel algorithm for solving the ECDF searching problem for a set of n points in two- and three-dimensional space on a Mesh-of\u00adProcessors of size n. However, it remained an open problem whether such an optimal solution exists for the d-dimensional ECDF searching problem for d4.<br>\nIn this paper we solve this problem by presenting an optimal O(&#8220;-Jri} time parallel solution to the d-dimensional ECDF searching problem for arbitrary dimension d= 0(1} on a Mesh-of-Processors of size n.<br>\nThe algorithm has several interesting implications. Among others the following problems can now be solved on a Mesh-of-Processors in (asymptotically optimal} time O(&#8216;Jn} for arbitrary dimension d=0(1}: the d-dimensional maximal element determination problem, the d-dimensional hypercube containment counting problem, and the d-dimensional hypercube intersection counting problem. The latter two problems can be mapped to the 2d-dimensional ECDF searching problem but require an efficient solution to this problem for at least d4.<\/p>\n<\/div>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/tr-121.pdf\">TR-121.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton University Technical Report TR-121 October 1987 n O(\u221an) Algorithm for the ECDF Searching Problem for Arbitrary Dimensions on a Mesh-of-Processors Frank Dehne &amp; Ivan Stojmenovic Abstract [1] presented an optimal O(&#8216;Jn} time parallel algorithm for solving the ECDF searching problem for a set of n points in two- and three-dimensional space on a Mesh-of\u00adProcessors [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":11827,"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-12629","page","type-page","status-publish","hentry"],"acf":{"cu_post_thumbnail":false},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12629","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=12629"}],"version-history":[{"count":1,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12629\/revisions"}],"predecessor-version":[{"id":12630,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12629\/revisions\/12630"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/11827"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=12629"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=12629"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}