Faster Approximation of Max Flow for Directed Graphs

TL;DR

This paper introduces a nearly-linear time algorithm for approximating maximum flow in directed graphs, extending previous undirected graph methods to handle directed cases efficiently.

Contribution

It adapts and extends existing electrical flow-based algorithms to efficiently approximate max flow in directed graphs, a significant advancement over prior approaches.

Findings

Nearly-linear time approximation algorithm for directed max flow

Extension of electrical flow methods to directed graphs

Improved computational efficiency over previous algorithms

Abstract

I extend the methods in "Electrical Flows, Laplacian Systems, and Faster Approximation of Maximum Flow in Undirected Graphs, with Paul Christiano, Jonathan Kelner, Daniel Spielman, and Shang-Hua Teng" to directed graphs with a variation of the framework in the paper, which lead to an algorithm that approximately solves the directed max flow problem in nearly-linear time.