Maximum flow in directed planar graphs with vertex capacities

Haim Kaplan, Yahav Nussbaum

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


In this paper we present an O(nlogn) algorithm for finding a maximum flow in a directed planar graph, where the vertices are subject to capacity constraints, in addition to the arcs. If the source and the sink are on the same face, then our algorithm can be implemented in O(n) time. For general (not planar) graphs, vertex capacities do not make the maximum flow problem more difficult, as there is a simple reduction that eliminates vertex capacities. However, this reduction does not preserve the planarity of the graph. The essence of our algorithm is a different reduction that does preserve the planarity, and can be implemented in linear time. For the special case of undirected planar graph, an algorithm with the same time complexity was recently claimed, but we show that it has a flaw.

Original languageEnglish
Title of host publicationAlgorithms - ESA 2009 - 17th Annual European Symposium, Proceedings
Number of pages11
StatePublished - 2009
Event17th Annual European Symposium on Algorithms, ESA 2009 - Copenhagen, Denmark
Duration: 7 Sep 20099 Sep 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5757 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference17th Annual European Symposium on Algorithms, ESA 2009


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