{"id":3895,"date":"2016-05-20T10:41:02","date_gmt":"2016-05-20T09:41:02","guid":{"rendered":"http:\/\/smart--grid.net\/?page_id=3895"},"modified":"2022-12-03T22:59:06","modified_gmt":"2022-12-03T21:59:06","slug":"algorithme-de-busacker-gowen","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/en\/maximum-flow-problem\/busacker-gowen-algorithm\/","title":{"rendered":"Busacker Gowen algorithm"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"3895\" class=\"elementor elementor-3895\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4fb8473 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4fb8473\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-c07a970\" data-id=\"c07a970\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d2f7fcd elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"d2f7fcd\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/en\/maximum-flow-problem\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Maximum flow problem<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column 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class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-5003641\" data-id=\"5003641\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-86a285d elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"86a285d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/fr.wikipedia.org\/wiki\/Algorithme_de_Busacker_et_Gowen\" target=\"_blank\" rel=\"noopener\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Wiki<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-55f8c26 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"55f8c26\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-3119e1a0\" data-id=\"3119e1a0\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-71ceb216 elementor-widget elementor-widget-text-editor\" data-id=\"71ceb216\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewbox=\"0 0 24 24\" version=\"1.2\" baseprofile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/complex-systems-ai.com\/en\/maximum-flow-problem\/busacker-gowen-algorithm\/#Algorithme-de-Busacker-Gowen\" >Busacker Gowen algorithm<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Algorithme-de-Busacker-Gowen\"><\/span>Busacker Gowen algorithm<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Also known as Roy&#039;s algorithm, Busacker Gowen&#039;s algorithm calculates a <a href=\"https:\/\/complex-systems-ai.com\/en\/maximum-flow-problem\/\">maximum flow<\/a> at minimal cost.<\/p>\n\n<div style=\"padding: 5px; background-color: #d5edff; border: 2px solid #3c95e8; -moz-border-radius: 9px; -khtml-border-radius: 9px; -webkit-border-radius: 9px; border-radius: 9px;\">The principle is simple, the search for the increasing path is done by a calculation of <a href=\"https:\/\/complex-systems-ai.com\/en\/graph-theory-path-search\/\">shortest way<\/a> (lowest cost path). The optimality criteria are equivalent to the flow problem.<\/div>\n\n<p>The algorithm is summarized as follows:<\/p>\n\n<div style=\"padding: 3px; border: 2px dotted #a5a5a5; background-color: #f6f9fa;\">\n<ul>\n<li>Build a <a href=\"https:\/\/complex-systems-ai.com\/en\/graph-theory-2\/\">graph<\/a> of pcc (shortest path) from the flow deviation graph\n<ul>\n<li>arc identical to the deviation graph<\/li>\n<li>price corresponding to the original arc if in the same direction, otherwise reverse<\/li>\n<\/ul>\n<\/li>\n<li>Look for a pcc from s to t\n<ul>\n<li>if it exists, it is the increasing path, the saturated one and return to the previous step<\/li>\n<li>if there is no path, end of the algorithm.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone wp-image-9863 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/09\/2-Premiere-iteration-de-lalgorithme-de-Busacker-et-Gowen.jpg\" alt=\"busacker gowen algorithm roy flow algorithm maximum minimum cost min cost flow\" width=\"601\" height=\"255\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/09\/2-Premiere-iteration-de-lalgorithme-de-Busacker-et-Gowen.jpg 601w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/09\/2-Premiere-iteration-de-lalgorithme-de-Busacker-et-Gowen-300x127.jpg 300w\" sizes=\"(max-width: 601px) 100vw, 601px\" \/><\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Maximum Flow Problem Home Page Wiki Busacker Gowen&#039;s Algorithm Also known as Roy&#039;s algorithm, Busacker Gowen&#039;s algorithm allows \u2026 <\/p>","protected":false},"author":1,"featured_media":0,"parent":3587,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-3895","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/3895","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/comments?post=3895"}],"version-history":[{"count":4,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/3895\/revisions"}],"predecessor-version":[{"id":17932,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/3895\/revisions\/17932"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/3587"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/media?parent=3895"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}