{"id":12729,"date":"2021-11-17T19:12:26","date_gmt":"2021-11-18T00:12:26","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=12729"},"modified":"2026-06-02T14:59:26","modified_gmt":"2026-06-02T18:59:26","slug":"tr-238-finding-the-extrema-of-a-distributed-multiset","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1994\/tr-238-finding-the-extrema-of-a-distributed-multiset\/","title":{"rendered":"TR-238: Finding the Extrema of a Distributed Multiset"},"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-238: Finding the Extrema of a Distributed Multiset\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-1994\/\">Technical Report<\/a> <strong>TR-238<\/strong><br>\nMarch 1994<\/p>\n\n\n\n<h2 id=\"finding-the-extrema-of-a-distributed-multiset\" class=\"wp-block-heading tr_t1\">Finding the Extrema of a Distributed Multiset<\/h2>\n\n\n\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">Paola Alimonti, Paola Flocchini , Nicola Santoro<\/div>\n<\/div>\n<\/div>\n\n\n\n<div>\n<h3>Abstract<\/h3>\n<p>We consider the problem of \fnding the extrema of a distributed multiset in a ring; that is, of determining the minimum and the maximum values, xmin&nbsp;and xmax, of a multiset X = {x0,x2&#8230; xn-1}, whose elements are drawn from a totally ordered universe U and stored at the n entities of a ring network.This problem is unsolvable if the ring size is not known to the entities, and has complexity \u0002O(n2) in the case of asynchronous rings of known size.<\/p>\n<p>We show that, in synchronous rings of known size, this problem can always be solved in O((c+log n)\u0001n) bits and O(n\u0001c\u0001x1\/c&nbsp;) time for any integer c &gt; 0, where x = Max{|xmin|, |xmax|}. The previous solutions required O(n2) bits and the same amount of time.Based on these results, we also present a bit optimal solution to the problem of \ffinding the multiplicity of the extrema.<\/p>\n<\/div>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/TR238.pdf\">TR-238.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton University Technical Report TR-238 March 1994 Finding the Extrema of a Distributed Multiset Paola Alimonti, Paola Flocchini , Nicola Santoro Abstract We consider the problem of \fnding the extrema of a distributed multiset in a ring; that is, of determining the minimum and the maximum values, xmin&nbsp;and xmax, of a multiset X = {x0,x2&#8230; [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":11914,"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-12729","page","type-page","status-publish","hentry"],"acf":{"cu_post_thumbnail":false},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12729","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=12729"}],"version-history":[{"count":1,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12729\/revisions"}],"predecessor-version":[{"id":12730,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12729\/revisions\/12730"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/11914"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=12729"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=12729"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}