 
Summary: Hardness of the Undirected EdgeDisjoint Paths Problem
Matthew Andrews
andrews@research.belllabs.com
Lisa Zhang
ylz@research.belllabs.com
Bell Laboratories
600700 Mountain Avenue
Murray Hill, NJ 07974
January 25, 2005
Abstract
We show that there is no log 1
3
\Gamma'' M approximation for the undirected EdgeDisjoint Paths
problem unless NP ` ZPT IME(n polylog n ), where M is the size of the graph and '' is any
positive constant. This hardness result also applies to the undirected AllorNothing Multicom
modity Flow problem and the undirected NodeDisjoint Paths problem.
1 Introduction
Consider an undirected graph G and a set f(s i ; t i )g of sourcesink pairs. In the undirected Edge
Disjoint Paths problem (EDP) we wish to connect as many of these pairs as possible using edge
disjoint paths. EDP is generally regarded as one of the ``classic'' NPhard problems. Past work on
