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Hardness of the EdgeDisjoint Paths Problem with Congestion Matthew Andrews

Summary: Hardness of the Edge­Disjoint Paths Problem with Congestion
Matthew Andrews
Lisa Zhang
Bell Laboratories
600­700 Mountain Avenue
Murray Hill, NJ 07974
April 26, 2005
In the Edge­Disjoint Paths problem with Congestion (EDPwC), we are given a graph with M edges
and a set of terminal pairs. The objective is to route as many terminal pairs as possible subject to the
constraint that at most w demands can be routed through any edge in the graph. In this paper, we study
the hardness of EDPwC in undirected graphs. We show that for any constant '' ? 0 and any conges­
tion w = o(log log M= log log log M) there is no log
w+1 M­approximation algorithm for EDPwC, unless
NP ` ZPT IME(n polylog n ). For larger congestions w Ÿ fl log log M= log log log M for some constant
fl, we obtain superconstant inapproximability ratios. Our reduction makes use of the Raz verifier and builds
upon the hardness for a related congestion minimization problem [1].


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


Collections: Mathematics; Computer Technologies and Information Sciences