Multiple-Source Multiple-Sink Maximum Flow in Directed Planar Graphs in Near-Linear Time

Abstract

We give an O(n log^3 n) algorithm that, given an n-node directed planar graph with arc capacities, a set of source nodes, and a set of sink nodes, finds a maximum flow from the sources to the sinks. Previously, the fastest algorithms known for this problem were those for general graphs.

18 pages, 1 figure