{"id":12671,"date":"2021-11-15T18:38:22","date_gmt":"2021-11-15T23:38:22","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=12671"},"modified":"2026-06-02T14:59:26","modified_gmt":"2026-06-02T18:59:26","slug":"tr-136-optimal-visibility-algorithms-for-binary-images-on-the-hypercube","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1988\/tr-136-optimal-visibility-algorithms-for-binary-images-on-the-hypercube\/","title":{"rendered":"TR-136: Optimal Visibility Algorithms for Binary Images on the Hypercube"},"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-136: Optimal Visibility Algorithms for Binary Images on the Hypercube\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-1988\/\">Technical Report<\/a> <strong>TR-136<\/strong><br>\nApril 1988<\/p>\n\n\n\n<h2 id=\"optimal-visibility-algorithms-for-binary-images-on-the-hypercube\" class=\"wp-block-heading tr_t1\">Optimal Visibility Algorithms for Binary Images on the Hypercube<\/h2>\n\n\n\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">Frank Dehne, Quoc T. Pham, Ivan Stojmenovic<\/div>\n<\/div>\n<\/div>\n\n\n\n<div>\n<h3>Abstract<\/h3>\n<p>Consider a nxn binary image. Given a direction D, the parallel visibility<br>\nproblem consists of determining for each pixel of the image the portion that is visible<br>\n(i.e., not obstructed by any other black pixel of the image) in direction D from infinity. A related problem, referred to as point visibility, is to compute for each pixel the<br>\nportion that is visible from a given point p.<br>\nIn this paper, we derive O(logn) time SIMD algorithms for each of these two<br>\nproblems on the hypercube where a processor is assigned to every pixel of the image. Since the worst case communication distance of two processors in a n2-processor hypercube is 2 log n, it follows thqt both of the above algorithms are asymptotically optimal.<\/p>\n<\/div>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/tr-136.pdf\">TR-136.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton University Technical Report TR-136 April 1988 Optimal Visibility Algorithms for Binary Images on the Hypercube Frank Dehne, Quoc T. Pham, Ivan Stojmenovic Abstract Consider a nxn binary image. Given a direction D, the parallel visibility problem consists of determining for each pixel of the image the portion that is visible (i.e., not obstructed by [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":11829,"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-12671","page","type-page","status-publish","hentry"],"acf":{"cu_post_thumbnail":false},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12671","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=12671"}],"version-history":[{"count":3,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12671\/revisions"}],"predecessor-version":[{"id":12679,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12671\/revisions\/12679"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/11829"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=12671"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=12671"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}