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ECCC
2007

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

9 years 1 months ago
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...
Matthew Andrews, Julia Chuzhoy, Venkatesan Guruswa
Added 18 Dec 2010
Updated 18 Dec 2010
Type Journal
Year 2007
Where ECCC
Authors Matthew Andrews, Julia Chuzhoy, Venkatesan Guruswami, Sanjeev Khanna, Kunal Talwar, Lisa Zhang
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