{"id":12565,"date":"2021-11-13T16:24:58","date_gmt":"2021-11-13T21:24:58","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=12565"},"modified":"2026-06-02T14:59:26","modified_gmt":"2026-06-02T18:59:26","slug":"tr-55-an-efficient-implicit-double-ended-priority-queue","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1984\/tr-55-an-efficient-implicit-double-ended-priority-queue\/","title":{"rendered":"TR-55: An Efficient, Implicit Double-Ended Priority Queue"},"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-55: An Efficient, Implicit Double-Ended Priority Queue\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-1984\/\">Technical Report<\/a> TR-55<br>\nJuly 1984<\/p>\n\n\n\n<h2 id=\"an-efficient-implicit-double-ended-priority-queue\" class=\"wp-block-heading tr_t1\">An Efficient, Implicit Double-Ended Priority Queue<\/h2>\n\n\n\n<p>M.D. Atkinson,, J\u00f6rg-R\u00fcdiger Sack, Nicola Santoro, T. Strothotte<\/p>\n\n\n\n<h3 id=\"abstract\" class=\"wp-block-heading\">Abstract<\/h3>\n\n\n\n<p>A simple implementation of double-ended priority queues is presented. The proposed structure, calles a min-max heap, can be built in linear time; in contrast to conventional heaps, it allows both FindMin and FindMax to be performed in constant time; Insert, DeleteMin, and DeleteMax operations can be performed in logarithmic time. Min-max heaps can be generalized to support other similar order-statistics operations efficiently (e.g., constant time FindMedian and Logarithmic time DeleteMedian); furthermore, the notion of min-max ordering can be extended to other heap-ordered structures, such as leftist trees.<\/p>\n\n\n\n<h3 id=\"download\" class=\"wp-block-heading\">Download<\/h3>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/TR-55.pdf\">TR-55.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton University Technical Report TR-55 July 1984 An Efficient, Implicit Double-Ended Priority Queue M.D. Atkinson,, J\u00f6rg-R\u00fcdiger Sack, Nicola Santoro, T. Strothotte Abstract A simple implementation of double-ended priority queues is presented. The proposed structure, calles a min-max heap, can be built in linear time; in contrast to conventional heaps, it allows both FindMin and FindMax [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":11787,"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":[88],"class_list":["post-12565","page","type-page","status-publish","hentry","cu_page_type-technical-report"],"acf":{"cu_post_thumbnail":false},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12565","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=12565"}],"version-history":[{"count":1,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12565\/revisions"}],"predecessor-version":[{"id":12567,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12565\/revisions\/12567"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/11787"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=12565"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=12565"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}