{"id":12786,"date":"2021-11-21T16:52:30","date_gmt":"2021-11-21T21:52:30","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=12786"},"modified":"2026-06-02T14:59:25","modified_gmt":"2026-06-02T18:59:25","slug":"tr-95-14-a-randomized-parallel-3d-convex-hull-algorithm-for-coarse-grained-multicomputers","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1995\/tr-95-14-a-randomized-parallel-3d-convex-hull-algorithm-for-coarse-grained-multicomputers\/","title":{"rendered":"TR-95-14: A Randomized Parallel 3D Convex Hull Algorithm for Coarse Grained Multicomputers"},"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-95-14: A Randomized Parallel 3D Convex Hull Algorithm for Coarse Grained Multicomputers\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-95-14<br>\nJune 1995<\/p>\n\n\n\n<h2 id=\"a-randomized-parallel-3d-convex-hull-algorithm-for-coarse-grained-multicomputers\" class=\"wp-block-heading tr_t1\">A Randomized Parallel 3D Convex Hull Algorithm for Coarse Grained Multicomputers<\/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\">Frank Dehne, Xiaotie Deng, Patrick Dymond, Andreas Fabri, Ashfaq A. Khokhar<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div>\n<h3>Abstract<\/h3>\n<\/div>\n\n\n\n<p class=\"tr_abstract\">We present a randomized parallel algorithm for constructing the 3D convex hull on a generic p-processor coarse grained multicomputer with arbitrary interconnection network and n=p local memory per processor, where n \/ p \u0015\u2265 p2+e\u000f (for some arbitrarily small e\u000f &gt; 0). For any given set of n points in 3-space, the algorithm computes the 3D convex hull, with high probability, in O( (n log n) \/ p ) local computation time and O(1) communication phases with at most O( n \/ p ) data sent\/received by each processor. That is, with high probability, the algorithm computes the 3D convex hull of an arbitrary point set in time O( (n log n) \/ p + T&nbsp;n,p), where Tn,p&nbsp;denotes the time complexity of one communication phase.In the terminology of the BSP model, our algorithm requires, with high probability, O(1) supersteps and a synchronization period O\u0002((n log n) \/ p ). In the LogP model, the execution time of our algorithm is asymptotically optimal for several architectures.<\/p>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/TR-95-14.pdf\">TR-95-14.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton University Technical Report TR-95-14 June 1995 A Randomized Parallel 3D Convex Hull Algorithm for Coarse Grained Multicomputers Frank Dehne, Xiaotie Deng, Patrick Dymond, Andreas Fabri, Ashfaq A. Khokhar Abstract We present a randomized parallel algorithm for constructing the 3D convex hull on a generic p-processor coarse grained multicomputer with arbitrary interconnection network and n=p [&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-12786","page","type-page","status-publish","hentry"],"acf":{"cu_post_thumbnail":false},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12786","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=12786"}],"version-history":[{"count":1,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12786\/revisions"}],"predecessor-version":[{"id":12787,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12786\/revisions\/12787"}],"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=12786"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=12786"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}