Routing Symmetric Demands in Directed Minor-Free Graphs with Constant Congestion

TL;DR

This paper extends polylogarithmic approximation algorithms with constant congestion for routing symmetric demands to directed minor-free graphs, broadening the scope from planar graphs.

Contribution

It introduces a polylogarithmic approximation with constant congestion for symmetric demand routing in directed minor-free graphs, generalizing previous planar graph results.

Findings

Achieved polylogarithmic approximation with constant congestion for directed minor-free graphs.

Extended results from planar graphs to all minor-free graphs.

Improved understanding of routing complexity in directed graphs.

Abstract

The problem of routing in graphs using node-disjoint paths has received a lot of attention and a polylogarithmic approximation algorithm with constant congestion is known for undirected graphs [Chuzhoy and Li 2016] and [Chekuri and Ene 2013]. However, the problem is hard to approximate within polynomial factors on directed graphs, for any constant congestion [Chuzhoy, Kim and Li 2016]. Recently, [Chekuri, Ene and Pilipczuk 2016] have obtained a polylogarithmic approximation with constant congestion on directed planar graphs, for the special case of symmetric demands. We extend their result by obtaining a polylogarithmic approximation with constant congestion on arbitrary directed minor-free graphs, for the case of symmetric demands.