Inapproximability of edge-disjoint paths and low congestion routing on undirected graphs

In the undirected Edge-Disjoint Paths problem with Congestion (EDPwC), we are given an undirected graph with V nodes, a set of terminal 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 Edge-Disjoint Paths (EDP) problem. In this paper, we study the hardness of EDPwC in undirected graphs. Our main result is that for every ε > 0 there exists an α > 0 such that for 1 c α log log V log log log V , it is hard to distinguish between instances where we can route all terminal pairs on edgedisjoint paths, and instances where we can route at most a 1/(log V ) 1−ε c+2 fraction of the terminal pairs, even if we allow congestion c. This implies a (log V ) 1−ε c+2 hardness of approximation for EDPwC and an Ω(log log V/ log log log V ) hardness of approximation for the undirected congestion minimization...

• Type: Journal
• Year: 2007
• Where: ECCC
• Authors: Matthew Andrews, Julia Chuzhoy, Venkatesan Guruswami, Sanjeev Khanna, Kunal Talwar, Lisa Zhang
• Keywords: ECCC 2007, Edge-disjoint Paths, Undirected Edge-disjoint Paths, Undirected Graphs