Faster Approximation Schemes for Fractional Multicommodity Flow Problems via Dynamic Graph Algorithms

TL;DR

This paper introduces faster approximation algorithms for fractional multicommodity flow problems by integrating dynamic graph algorithms, achieving near-optimal running times under certain input conditions.

Contribution

It presents novel (1-eps)-approximation schemes that improve upon previous methods by matching the flow-decomposition barrier for multicommodity flows.

Findings

Algorithms run in near-optimal time bounds

Approximation quality is (1-eps)

Applicable to polynomially bounded input sizes

Abstract

We combine the work of Garg and Konemann, and Fleischer with ideas from dynamic graph algorithms to obtain faster (1-eps)-approximation schemes for various versions of the multicommodity flow problem. In particular, if eps is moderately small and the size of every number used in the input instance is polynomially bounded, the running times of our algorithms match - up to poly-logarithmic factors and some provably optimal terms - the Omega(mn) flow-decomposition barrier for single-commodity flow.