{"id":15004,"date":"2022-06-16T19:44:05","date_gmt":"2022-06-16T23:44:05","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=15004"},"modified":"2026-06-09T10:04:14","modified_gmt":"2026-06-09T14:04:14","slug":"tr-196-lights-walls-and-bricks","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1991\/tr-196-lights-walls-and-bricks\/","title":{"rendered":"TR-196: Lights, Walls and Bricks"},"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-196: Lights, Walls and Bricks\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-1991\/\">Technical Report<\/a>&nbsp;<strong>TR-196<\/strong><br>October 1991<\/p>\n\n\n\n<h2 id=\"lights-walls-and-bricks\" class=\"wp-block-heading\">Lights, Walls and Bricks<\/h2>\n\n\n\n<p>J. Czyzowicz, E. Rivera-Campo, N. Santoro, J. Urrutia, J. Zaks<\/p>\n\n\n\n<h3 id=\"abstract\" class=\"wp-block-heading\">Abstract<\/h3>\n\n\n\n<p>Consider a rectangular art gallery divided into n rectangular rooms, such that any two rooms sharing a wall in common have a door connecting them. How many guards need to be stationed in the gallery so as to protect all of the rooms in our gallery? Notice that if a guard is stationed at a<br>door, he will be able to guard two rooms. Our main aim in this paper is to show that r n\/2 l guards are always sufficient to protect all rooms in a rectangular art gallery. Extensions of our result are obtained for non rectangular galleries and for 3-dimensional art galleries.<\/p>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/TR-196.pdf\">TR-196.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton UniversityTechnical Report&nbsp;TR-196October 1991 Lights, Walls and Bricks J. Czyzowicz, E. Rivera-Campo, N. Santoro, J. Urrutia, J. Zaks Abstract Consider a rectangular art gallery divided into n rectangular rooms, such that any two rooms sharing a wall in common have a door connecting them. How many guards need to be stationed in the gallery so [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":11908,"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-15004","page","type-page","status-publish","hentry"],"acf":{"cu_post_thumbnail":""},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/15004","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=15004"}],"version-history":[{"count":2,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/15004\/revisions"}],"predecessor-version":[{"id":24514,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/15004\/revisions\/24514"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/11908"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=15004"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=15004"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}