{"id":12801,"date":"2021-11-21T17:05:30","date_gmt":"2021-11-21T22:05:30","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=12801"},"modified":"2026-06-02T14:59:25","modified_gmt":"2026-06-02T18:59:25","slug":"tr-95-22-approximate-maxima-finding-of-continuous-functions-under-restricted-budget","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1995\/tr-95-22-approximate-maxima-finding-of-continuous-functions-under-restricted-budget\/","title":{"rendered":"TR-95-22: Approximate Maxima Finding of Continuous Functions under Restricted Budget"},"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-95-22: Approximate Maxima Finding of Continuous Functions under Restricted Budget\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-1995\/\">Technical Report<\/a> TR-95-22<br>\nNovember 1995<\/p>\n\n\n\n<h2 id=\"approximate-maxima-finding-of-continuous-functions-under-restricted-budget\" class=\"wp-block-heading tr_t1\">Approximate Maxima Finding of Continuous Functions under Restricted Budget<\/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\">Evangelos Kranakis, Danny Krizanc, Andrzej Pelc, David Peleg<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div>\n<h3>Abstract<\/h3>\n<\/div>\n\n\n\n<div class=\"tr_abstract\">\n<p>A function is distributed among nodes of a graph in a continuous way, i.e., such that the di\u000berence between values stored at adjacent nodes is small. The goal is to \fnd a node of maximum value by probing some nodes under a restricted budget. Every node has an associated cost which has to be paid for probing it and a probe reveals the value of the node. If the total budget is too small to allow probing every node, it is impossible to \fnd the maximum value in the worst case. Hence we seek an Approximate Maxima Finding (AMF) algorithm that o\u000bers the best worst-case guarantee g, i.e., for any continuous distribution of values it \fnds a node whose value di\u000bers from the maximum value by at most g.Approximate Maxima Finding in graphs is related to a generalization of the multi-center problem and we get new results for this problem as well. For example, we givea polynomial algorithm to \fnd a minimum cost solution for the multicenter problem on a tree, with arbitrary node costs.<\/p>\n<\/div>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/TR-95-22.pdf\">TR-95-22.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton University Technical Report TR-95-22 November 1995 Approximate Maxima Finding of Continuous Functions under Restricted Budget Evangelos Kranakis, Danny Krizanc, Andrzej Pelc, David Peleg Abstract A function is distributed among nodes of a graph in a continuous way, i.e., such that the di\u000berence between values stored at adjacent nodes is small. The goal is to [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":11736,"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-12801","page","type-page","status-publish","hentry"],"acf":{"cu_post_thumbnail":false},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12801","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=12801"}],"version-history":[{"count":1,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12801\/revisions"}],"predecessor-version":[{"id":12802,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12801\/revisions\/12802"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/11736"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=12801"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=12801"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}