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)­

Source: Andrews, Matthew - Mathematics of Networks and Systems, Mathematical Sciences Research Center, Bell Laboratories
Khanna, Sanjeev - Department of Computer and Information Science, University of Pennsylvania
Pennsylvania, University of - Department of Computer and Information Science, Database Research Group

Collections: Computer Technologies and Information Sciences; Mathematics