{"id":12631,"date":"2021-11-14T20:25:51","date_gmt":"2021-11-15T01:25:51","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=12631"},"modified":"2026-06-02T14:59:26","modified_gmt":"2026-06-02T18:59:26","slug":"tr-123-solving-visibility-and-separability-problems-on-a-mesh-of-processors","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1987\/tr-123-solving-visibility-and-separability-problems-on-a-mesh-of-processors\/","title":{"rendered":"TR-123: Solving Visibility and Separability Problems 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-123: Solving Visibility and Separability Problems 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-123<\/strong><br>\nNovember 1987<\/p>\n\n\n\n<h2 id=\"solving-visibility-and-separability-problems-on-a-mesh-of-processors\" class=\"wp-block-heading tr_t1\">Solving Visibility and Separability Problems on a Mesh-of-Processors<\/h2>\n\n\n\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">Frank Dehne<\/div>\n<\/div>\n\n\n\n<div>\n<h3>Abstract<\/h3>\n<p>In this paper we study parallel algorithms for the Mesh-of-Processors architecture to solve visibility as well as related separability problems for sets of simple polygons in the plane; in particular, we solve the following problems:<br>\n( 1 ) compute for a point p inside a N-vertex simple polygon with holes the visibility polygon containing all points visible from p<\/p>\n<p>( 2) for the parallel visibility model (visibility from a point with infinite distance) compute the portion of a N-vertex simple polygon visible in a given direction d and the visibility hull with respect to direction d<\/p>\n<p>(3) determine whether two N-vertex simple polygons are separable (without collision) by a single translation in a given direction d<\/p>\n<p>( 4 ) determine for a set of M N-vertex simple polygons whether they are sequentially separable in a given direction d, i.e. whether there exists a sequence of translations in direction d, one for each polygon, which allows to separate them without collisions between polygons.<\/p>\n<p>The parallel algorithms presented in this paper have an asymptotically optimal time complexity of O(&#8211;IN) for problems 1-3 and O(\u2713M N) for problem 4, respectively, and require a linear number of processing elements ..<\/p>\n<\/div>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/tr-123.pdf\">TR-123.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton University Technical Report TR-123 November 1987 Solving Visibility and Separability Problems on a Mesh-of-Processors Frank Dehne Abstract In this paper we study parallel algorithms for the Mesh-of-Processors architecture to solve visibility as well as related separability problems for sets of simple polygons in the plane; in particular, we solve the following problems: ( 1 [&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-12631","page","type-page","status-publish","hentry"],"acf":{"cu_post_thumbnail":false},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12631","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=12631"}],"version-history":[{"count":2,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12631\/revisions"}],"predecessor-version":[{"id":12635,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12631\/revisions\/12635"}],"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=12631"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=12631"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}