Maximum Flow in Directed Planar Graphs with Vertex Capacities

  • Haim Kaplan
  • Yahav Nussbaum
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5757)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Haim Kaplan
    • 1
  • Yahav Nussbaum
    • 1
  1. 1.The Blavatnik School of Computer ScienceTel Aviv UniversityTel AvivIsrael

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