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Hardness of the Undirected EdgeDisjoint Paths Problem Matthew Andrews

Summary: Hardness of the Undirected Edge­Disjoint Paths Problem
Matthew Andrews
Lisa Zhang
Bell Laboratories
600­700 Mountain Avenue
Murray Hill, NJ 07974
January 25, 2005
We show that there is no log 1
\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


Source: Andrews, Matthew - Mathematics of Networks and Systems, Mathematical Sciences Research Center, Bell Laboratories


Collections: Mathematics; Computer Technologies and Information Sciences