{"id":14759,"date":"2022-05-26T22:59:56","date_gmt":"2022-05-27T02:59:56","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=14759"},"modified":"2026-06-09T11:08:06","modified_gmt":"2026-06-09T15:08:06","slug":"tr-160-disassembling-two-dimensional-composite-parts-via-translations","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1989\/tr-160-disassembling-two-dimensional-composite-parts-via-translations\/","title":{"rendered":"TR-160: Disassembling Two-Dimensional Composite Parts Via Translations"},"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-160: Disassembling Two-Dimensional Composite Parts Via Translations\n                    <\/h1>\n                \n                                \n                            <\/header>\n\n                    <\/div>\n\n            <\/div>\n\n    <\/div>\n<\/section>\n\n\n\n<p>Carleton University<br><a href=\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1989\/\">Technical Report<\/a>&nbsp;<strong>TR-160<\/strong><br>June 1989<\/p>\n\n\n\n<h2 id=\"epsilon-optimal-stubborn-learning-mechanisms\" class=\"wp-block-heading\">Epsilon-Optimal Stubborn Learning Mechanisms<\/h2>\n\n\n\n<p>Doron Nussbaum &amp; J\u00f6rg-R. Sack<\/p>\n\n\n\n<h3 id=\"abstract\" class=\"wp-block-heading\">Abstract<\/h3>\n\n\n\n<p>This paper deals with the computational complexity of disassembling 2-dimensional composite parts (comprised of simple polygons) via collision-free translations. The first result of this paper is an O(Mn + M log M) algorithm for computing a sequence of translations (performed in a common direction) to disassemble composite parts. The algorithm improves on the O(M n log Mn) bound previously established for this problem and is easily seen to be optimal. The algorithm solves the problem posed by Nurmi and by Toussaint.<br>The second result of this paper is an Q.(Mn + M log M) lower bound proof for the problem of detecting whether a composite part can be disassembled, or contains interlocking subparts. Thus, detecting the existence of a disassembly sequence is as hard as computing one. As a consequence, the algorithm for computing a disassembly sequence is optimal also for the detecting problem.<\/p>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/TR-160.pdf\">TR-160.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton UniversityTechnical Report&nbsp;TR-160June 1989 Epsilon-Optimal Stubborn Learning Mechanisms Doron Nussbaum &amp; J\u00f6rg-R. Sack Abstract This paper deals with the computational complexity of disassembling 2-dimensional composite parts (comprised of simple polygons) via collision-free translations. The first result of this paper is an O(Mn + M log M) algorithm for computing a sequence of translations (performed in [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":11903,"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-14759","page","type-page","status-publish","hentry"],"acf":{"cu_post_thumbnail":""},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/14759","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=14759"}],"version-history":[{"count":2,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/14759\/revisions"}],"predecessor-version":[{"id":24548,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/14759\/revisions\/24548"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/11903"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=14759"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=14759"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}