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

TL;DR

This paper presents a near-linear time algorithm for computing maximum flow in directed planar graphs with multiple sources and sinks, improving efficiency over previous general graph algorithms.

Contribution

The paper introduces an O(n log^3 n) algorithm specifically for maximum flow in directed planar graphs with multiple sources and sinks, surpassing prior general graph methods.

Findings

Achieved near-linear time complexity for the problem

Improved upon previous algorithms for general graphs

Demonstrated efficiency in directed planar graph scenarios

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.