{"id":4626,"date":"2015-05-22T17:44:35","date_gmt":"2015-05-22T15:44:35","guid":{"rendered":"http:\/\/pimedios.es\/?p=4626"},"modified":"2015-05-22T17:44:35","modified_gmt":"2015-05-22T15:44:35","slug":"red-de-flujo","status":"publish","type":"post","link":"http:\/\/pimedios.jesussoto.es\/?p=4626","title":{"rendered":"Red de Flujo"},"content":{"rendered":"<p><a href=\"http:\/\/pimedios.es\/wp-content\/uploads\/2015\/05\/tolstoi1930.png\"><img loading=\"lazy\" decoding=\"async\" class=\"  wp-image-4629 alignnone\" src=\"http:\/\/pimedios.es\/wp-content\/uploads\/2015\/05\/tolstoi1930-300x245.png\" alt=\"tolstoi1930\" width=\"246\" height=\"201\" srcset=\"http:\/\/pimedios.jesussoto.es\/wp-content\/uploads\/2015\/05\/tolstoi1930-300x245.png 300w, http:\/\/pimedios.jesussoto.es\/wp-content\/uploads\/2015\/05\/tolstoi1930.png 754w\" sizes=\"auto, (max-width: 246px) 100vw, 246px\" \/><\/a>Comencemos con explicando el t\u00e9rmino Red de flujo:<br \/>\n<iframe loading=\"lazy\" src=\"https:\/\/www.youtube.com\/embed\/GqnOL3SwuTM\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Como decimos en el v\u00eddeo, uno de los trabajos que dan salida al uso de las redes de flujo es el <a title=\"Algoritmo de Ford-Fulkerson\" href=\"http:\/\/es.wikipedia.org\/wiki\/Algoritmo_de_Ford-Fulkerson\">Algoritmo de Ford-Fulkerson<\/a>\u00a0para encontrar el flujo m\u00e1ximo de una red. Este algoritmo se publica en 1956 por\u00a0<a title=\"L. R. Ford, Jr.\" href=\"http:\/\/en.wikipedia.org\/wiki\/L._R._Ford,_Jr.\">L. R. Ford, Jr.<\/a>\u00a0 y\u00a0<a title=\"D. R. Fulkerson\" href=\"http:\/\/en.wikipedia.org\/wiki\/D._R._Fulkerson\">D. R. Fulkerson<\/a>, en el art\u00edculo <span class=\"reference-text\"><span class=\"citation journal\"><em>Maximal flow through a network<\/em> (<i><a title=\"Canadian Journal of Mathematics\" href=\"http:\/\/en.wikipedia.org\/wiki\/Canadian_Journal_of_Mathematics\">Canadian Journal of Mathematics<\/a><\/i> <b>8<\/b>: 399. <a title=\"Digital object identifier\" href=\"http:\/\/en.wikipedia.org\/wiki\/Digital_object_identifier\">doi<\/a>:<a class=\"external text\" href=\"http:\/\/dx.doi.org\/10.4153%2FCJM-1956-045-5\" rel=\"nofollow\">10.4153\/CJM-1956-045-5<\/a>)<\/span><\/span>.\u00a0Sin embargo, en el comienzo de la publicaci\u00f3n nos dice que plantean estudiar el problema, formulado por T.E. Harris, siguiente:<\/p>\n<blockquote><p>\u00abConsider a rail network connecting two cities by way of \u00a0number of\u00a0intermediate cities, where each link of the network has a number assigned to\u00a0it representing its capacity. Assuming a steady state condition, find a maximal\u00a0flow from one given city to the other.\u00bb<\/p><\/blockquote>\n<p>Este problema lo presenta\u00a0T.E. Harris en una correspondencia con F.S Ross sobre el trabajo que publican en 1955 (T.E. Harris, F.S. Ross, <em>Fundamentals of a Method for Evaluating Rail Net Capacities<\/em>, Research\u00a0Memorandum RM-1573, The RAND Corporation, Santa Monica, California, 1955). \u00a0Pero si tenemos que encontrar el inicio, debemos retroceder a 1930, cuando A.N. Tolstoi publica un trabajo sobre un problema del transporte (la figura de arriba pertenece al art\u00edculo).\u00a0Tolstoi trataba de analizar los problemas de las comunicaciones en la redes ferroviales sovi\u00e9ticas.<\/p>\n<p>El problema del transporte, que dar\u00eda paso al teor\u00eda de transporte, muy desarrollada en econom\u00eda, fue formulada por el matem\u00e1tico franc\u00e9s\u00a0 <a title=\"Gaspard Monge\" href=\"http:\/\/en.wikipedia.org\/wiki\/Gaspard_Monge\">Gaspard Monge<\/a>\u00a0en 1781. Pero en los a\u00f1os 20 del siglo pasado, A.N. Tolstoi realizar\u00eda los primeros trabajos para estudiar el problema del transporte matem\u00e1ticamente.<\/p>\n<p>Para m\u00e1s informaci\u00f3n ver\u00a0<span class=\"reference-text\"><a title=\"Alexander Schrijver\" href=\"http:\/\/en.wikipedia.org\/wiki\/Alexander_Schrijver\">Schrijver, Alexander<\/a>, <a class=\"external text\" href=\"http:\/\/books.google.com\/books?id=mqGeSQ6dJycC&amp;printsec=frontcover\" rel=\"nofollow\"><i>Combinatorial Optimization<\/i><\/a>, Berlin\u00a0; New York\u00a0: Springer, 2003. ISBN 3540443894.\u00a0<\/span><\/p>\n<blockquote><p>Esta entrada participa en la <a href=\"http:\/\/bit.ly\/1QSOXDc\">Edici\u00f3n 6.4: pseudoprimos<\/a> del Carnaval de Matem\u00e1ticas cuyo anfitri\u00f3n es <a href=\"http:\/\/pimedios.es\" target=\"_blank\">pimedios<\/a>.<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>Red de flujo, un paseo desde los trabajos de A.N. Tolstoi hasta el algoritmo de Ford\u2013Fulkerson.<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,9],"tags":[644,645],"class_list":["post-4626","post","type-post","status-publish","format-standard","hentry","category-historia","category-personajes","tag-algoritmo-de-ford-fulkerson","tag-red-de-flujo","entry"],"_links":{"self":[{"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/4626","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4626"}],"version-history":[{"count":3,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/4626\/revisions"}],"predecessor-version":[{"id":4630,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/4626\/revisions\/4630"}],"wp:attachment":[{"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4626"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4626"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4626"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}