Multiple-source multiple-sink maximum flow in planar graphs

Multiple-Source Multiple-Sink Maximum Flow in Directed Planar Graphs in $O(n^{1.5} \log n)$ Time

We give an O(n log n) algorithm that, given a 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.

Multiple-Source Multiple-Sink Maximum Flow in Directed Planar Graphs in O(n log n) Time

We give an O(n logn) algorithm that, given a 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.

Planar Maximum Flow - Multiple-Source Multiple-Sink Maximum Flow in Directed Planar Graphs

Multiple source, single sink maximum flow in a planar graph

We give an O(n logn) time algorithm for finding the maximum flow in a directed planar graph with multiple sources and a single sink. The techniques generalize to a subquadratic time algorithm for bounded genus graphs.

Multiple-Source Single-Sink Maximum Flow in Directed Planar Graphs in O(diameter · n log n) Time

We develop a new technique for computing maximum flow in directed planar graphs with multiple sources and a single sink that significantly deviates from previously known techniques for flow problems. This gives rise to an O(diameter · n logn) algorithm for the problem.