{"id":384,"date":"2013-04-11T14:08:48","date_gmt":"2013-04-11T14:08:48","guid":{"rendered":"http:\/\/corner.mimuw.edu.pl\/?p=384"},"modified":"2022-09-12T10:56:30","modified_gmt":"2022-09-12T10:56:30","slug":"presentation-monge-property-and-max-flows-in-planar-graphs","status":"publish","type":"post","link":"https:\/\/corner.mimuw.edu.pl\/?p=384","title":{"rendered":"Presentation: Monge Property and Max-Flows in Planar Graphs"},"content":{"rendered":"<p>If you are interested in max-flow computations in planar graphs, below is the talk I have given at <a href=\"http:\/\/worker2013.mimuw.edu.pl\/\">WORKER 2013<\/a>. It gives an overview of how to use shortest paths and Monge property to get the following three results:<\/p>\n<ul>\n<li>O(n log log n) time algorithm for undirected max-flow in planar graphs [1],<\/li>\n<li>almost linear time algorithm for all-source all-sink max-flow in undirected planar graphs, i.e., it computes Gumory-Hu tree [2],<\/li>\n<li>almost linear time algorithm for single-source all-sink max-flow in directed planar graphs [3].<\/li>\n<\/ul>\n<p><iframe loading=\"lazy\" src=\"http:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/04\/worker2.swf\" width=\"580\" height=\"435\" frameborder=\"0\" marginwidth=\"0\" scrolling=\"no\"><\/iframe><\/p>\n<p>[1] Giuseppe F. Italiano, Yahav Nussbaum, Piotr Sankowski, Christian Wulff-Nilsen: Improved algorithms for min cut and max flow in undirected planar graphs. STOC 2011: 313-322.<br \/>\n[2] Glencora Borradaile, Piotr Sankowski, Christian Wulff-Nilsen: Min st-cut Oracle for Planar Graphs with Near-Linear Preprocessing Time. FOCS 2010: 601-610.<br \/>\n[3] Jakub Lacki, Yahav Nussbaum, Piotr Sankowski, Christian Wulff-Nilsen: Single Source - All Sinks Max Flows in Planar Digraphs. FOCS 2012: 599-608.<br \/>\nIf you are interested in max-flow computations in planar graphs, below is the talk I have given at <a href=\"http:\/\/worker2013.mimuw.edu.pl\/\">WORKER 2013<\/a>. It gives an overview of how to use shortest paths and Monge property to get the following three results:<\/p>\n<ul>\n<li>O(n log log n) time algorithm for undirected max-flow in planar graphs [1],<\/li>\n<li>almost linear time algorithm for all-source all-sink max-flow in undirected planar graphs, i.e., it computes Gumory-Hu tree [2],<\/li>\n<li>almost linear time algorithm for single-source all-sink max-flow in directed planar graphs [3].<\/li>\n<\/ul>\n<p><iframe loading=\"lazy\" src=\"http:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/04\/worker2.swf\" width=\"580\" height=\"435\" frameborder=\"0\" marginwidth=\"0\" scrolling=\"no\"><\/iframe><\/p>\n<p>[1] Giuseppe F. Italiano, Yahav Nussbaum, Piotr Sankowski, Christian Wulff-Nilsen: Improved algorithms for min cut and max flow in undirected planar graphs. STOC 2011: 313-322.<br \/>\n[2] Glencora Borradaile, Piotr Sankowski, Christian Wulff-Nilsen: Min st-cut Oracle for Planar Graphs with Near-Linear Preprocessing Time. FOCS 2010: 601-610.<br \/>\n[3] Jakub Lacki, Yahav Nussbaum, Piotr Sankowski, Christian Wulff-Nilsen: Single Source - All Sinks Max Flows in Planar Digraphs. FOCS 2012: 599-608.<br \/>\nIf you are interested in max-flow computations in planar graphs, below is the talk I have given at <a href=\"http:\/\/worker2013.mimuw.edu.pl\/\">WORKER 2013<\/a>. It gives an overview of how to use shortest paths and Monge property to get the following three results:<br \/>\n- O(n log log n) time algorithm for undirected max-flow in planar graphs [1],<br \/>\n- almost linear time algorithm for all-source all-sink max-fl<\/p>\n<p><iframe loading=\"lazy\" src=\"http:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/04\/worker2.swf\" width=\"580\" height=\"435\" frameborder=\"0\" marginwidth=\"0\" scrolling=\"no\"><\/iframe><\/p>\n<p>[1] Giuseppe F. Italiano, Yahav Nussbaum, Piotr Sankowski, Christian Wulff-Nilsen: Improved algorithms for min cut and max flow in undirected planar graphs. STOC 2011: 313-322.<br \/>\n[2] Glencora Borradaile, Piotr Sankowski, Christian Wulff-Nilsen: Min st-cut Oracle for Planar Graphs with Near-Linear Preprocessing Time. FOCS 2010: 601-610.<br \/>\n[3] Jakub Lacki, Yahav Nussbaum, Piotr Sankowski, Christian Wulff-Nilsen: Single Source - All Sinks Max Flows in Planar Digraphs. FOCS 2012: 599-608.<\/p>\n<p>If you are interested in max-flow computations in planar graphs, below is the talk I have given at <a href=\"http:\/\/worker2013.mimuw.edu.pl\/\">WORKER 2013<\/a>. It gives an overview of how to use shortest paths and Monge property to get the following three results:<br \/>\n- O(n log log n) time algorithm for undirected max-flow in planar graphs [1],<br \/>\n- almost linear time algorithm for all-source all-sink max-flow in undirected planar graphs, i.e., it computes Gumory-Hu tree [2],<br \/>\n- almost linear time algorithm for single-source all-sink max-low in directed planar graphs [3].<\/p>\n<p><iframe loading=\"lazy\" src=\"http:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/04\/worker2.swf\" width=\"580\" height=\"435\" frameborder=\"0\" marginwidth=\"0\" scrolling=\"no\"><\/iframe><\/p>\n<p>[1] Giuseppe F. Italiano, Yahav Nussbaum, Piotr Sankowski, Christian Wulff-Nilsen: Improved algorithms for min cut and max flow in undirected planar graphs. STOC 2011: 313-322.<br \/>\n[2] Glencora Borradaile, Piotr Sankowski, Christian Wulff-Nilsen: Min st-cut Oracle for Planar Graphs with Near-Linear Preprocessing Time. FOCS 2010: 601-610.<br \/>\n[3] Jakub Lacki, Yahav Nussbaum, Piotr Sankowski, Christian Wulff-Nilsen: Single Source - All Sinks Max Flows in Planar Digraphs. FOCS 2012: 599-608.<\/p>\n<table>\n<tbody>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-370\" src=\"http:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/03\/cat.png\" alt=\"cat\" width=\"400\" height=\"354\" srcset=\"https:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/03\/cat.png 400w, https:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/03\/cat-300x265.png 300w, https:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/03\/cat-338x300.png 338w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/td>\n<td>row 1, celldf adsf sad fdsa fsda fsdf sadad sda dsa ds 2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table border=\"1\">\n<tbody>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-370\" src=\"http:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/03\/cat.png\" alt=\"cat\" width=\"400\" height=\"354\" srcset=\"https:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/03\/cat.png 400w, https:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/03\/cat-300x265.png 300w, https:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/03\/cat-338x300.png 338w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/td>\n<td>row 1, celldf adsf sad fdsa fsda fsdf sadad sda dsa ds 2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table border=\"1\">\n<tbody>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-370\" src=\"http:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/03\/cat.png\" alt=\"cat\" width=\"400\" height=\"354\" srcset=\"https:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/03\/cat.png 400w, https:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/03\/cat-300x265.png 300w, https:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/03\/cat-338x300.png 338w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/td>\n<td>row 1, celldf adsf sad fdsa fsda fsdf sadad sda dsa ds 2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>According to the report by Foundation for Polish Science working in Poland can be seen as hurting your scientific carrier (114873,10657310, Badacze_o_Polsce__praca_tam_moze_zaszkodzic_karierze.html\"&gt;article in polish).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-370\" src=\"http:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/03\/cat.png\" alt=\"cat\" width=\"400\" height=\"354\" srcset=\"https:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/03\/cat.png 400w, https:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/03\/cat-300x265.png 300w, https:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/03\/cat-338x300.png 338w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/p>\n<p>We do not really agree with it and the above meme was meant to be self-ironic. It of course could be better - as everywhere. Anyway, if you would like to see how it is to work in Poland we have two postdoc positions in algorithms open - <a href=\"http:\/\/paal.mimuw.edu.pl\/index.php?option=com_content&amp;view=article&amp;id=15&amp;Itemid=10\">see the call.<\/a><br \/>\nAccording to the report by Foundation for Polish Science working in Poland can be seen as hurting your scientific carrier (114873, 10657310,Badacze_o_Polsce__praca_tam_moze_zaszkodzic_karierze.html\"&gt;article in polish).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-370\" src=\"http:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/03\/cat.png\" alt=\"cat\" width=\"400\" height=\"354\" srcset=\"https:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/03\/cat.png 400w, https:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/03\/cat-300x265.png 300w, https:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/03\/cat-338x300.png 338w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/p>\n<p>We do not really agree with it and the above meme was meant to be self-ironic. It of course could be better - as everywhere. Anyway, if you would like to see how it is to work in Poland we have two postdoc positions in algorithms open - <a href=\"http:\/\/paal.mimuw.edu.pl\/index.php?option=com_content&amp;view=article&amp;id=15&amp;Itemid=10\">see the call.<\/a><br \/>\nIf you are interested in max-flow computations in planar graphs, below is the talk I have given at <a href=\"http:\/\/worker2013.mimuw.edu.pl\/\">WORKER 2013<\/a>. It gives an overview of how to use shortest paths and Monge property to get the following three results:<\/p>\n<ul>\n<li>O(n log log n) time algorithm for undirected max-flow in planar graphs [1],<\/li>\n<li>almost linear time algorithm for all-source all-sink max-flow in undirected planar graphs, i.e., it computes Gumory-Hu tree [2],<\/li>\n<li>almost linear time algorithm for single-source all-sink max-flow in directed planar graphs [3].<\/li>\n<\/ul>\n<p><iframe loading=\"lazy\" src=\"http:\/\/corner.mimuw.edu.pl\/wp-content\/uploads\/2013\/04\/worker2.swf\" width=\"580\" height=\"435\" frameborder=\"0\" marginwidth=\"0\" scrolling=\"no\"><\/iframe><\/p>\n<p>[1] Giuseppe F. Italiano, Yahav Nussbaum, Piotr Sankowski, Christian Wulff-Nilsen: Improved algorithms for min cut and max flow in undirected planar graphs. STOC 2011: 313-322.<br \/>\n[2] Glencora Borradaile, Piotr Sankowski, Christian Wulff-Nilsen: Min st-cut Oracle for Planar Graphs with Near-Linear Preprocessing Time. FOCS 2010: 601-610.<br \/>\n[3] Jakub Lacki, Yahav Nussbaum, Piotr Sankowski, Christian Wulff-Nilsen: Single Source - All Sinks Max Flows in Planar Digraphs. FOCS 2012: 599-608.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>If you are interested in max-flow computations in planar graphs, below is the talk I have given at WORKER 2013. It gives an overview of how to use shortest paths and Monge property to get the following three results: O(n &hellip; <a href=\"https:\/\/corner.mimuw.edu.pl\/?p=384\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/corner.mimuw.edu.pl\/index.php?rest_route=\/wp\/v2\/posts\/384"}],"collection":[{"href":"https:\/\/corner.mimuw.edu.pl\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/corner.mimuw.edu.pl\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/corner.mimuw.edu.pl\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/corner.mimuw.edu.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=384"}],"version-history":[{"count":9,"href":"https:\/\/corner.mimuw.edu.pl\/index.php?rest_route=\/wp\/v2\/posts\/384\/revisions"}],"predecessor-version":[{"id":1141,"href":"https:\/\/corner.mimuw.edu.pl\/index.php?rest_route=\/wp\/v2\/posts\/384\/revisions\/1141"}],"wp:attachment":[{"href":"https:\/\/corner.mimuw.edu.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=384"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/corner.mimuw.edu.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=384"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/corner.mimuw.edu.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=384"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}