 
Summary: Hardness of the Undirected EdgeDisjoint Paths Problem with Congestion
Matthew Andrews # Julia Chuzhoy + Sanjeev Khanna # Lisa Zhang #
Abstract
In the EdgeDisjoint Paths problem with Congestion
(EDPwC), we are given a graph with n nodes, a set of ter
minal pairs and an integer c. The objective is to route as
many terminal pairs as possible, subject to the constraint
that at most c demands can be routed through any edge in
the graph. When c = 1, the problem is simply referred to as
the EdgeDisjoint Paths (EDP) problem. In this paper, we
study the hardness of EDPwC in undirected graphs.
We obtain an improved hardness result for EDP, and
also show the first polylogarithmic integrality gaps and
hardness of approximation results for EDPwC. Specif
ically, we prove that EDP is (log 1
2 # n)hard to ap
proximate for any constant # > 0, unless NP #
ZPT IME(n polylog n ). We also show that for any conges
tion c = o(log log n/ log log log n), there is no (log 1#
c+1 n)
