We study the approximability of the All-or-Nothing mul-ticommodity flow problem in directed graphs with symmetric demand pairs (SymANF). The input consists of a directed graph G = (V, E) and a collection of (unordered) pairs of nodes M = {s_1t_1, s_2t_2,..., s_kt_k}. A subset M' of the pairs is routable if there is a feasible multicommodity flow in G such that, for each pair s_it_i ∈ M', the amount of flow from s_i to t_i is at least one and the amount of flow from t_i to s_i is at least one. The goal is to find a maximum cardinality subset of the given pairs that can be routed. Our main result is a poly-logarithmic approximation with constant congestion for SymANF. We obtain this result by extending the well-linked decomposition framework of to the directed graph setting with symmetric demand pairs. We point out the importance of studying routing problems in this setting and the relevance of our result to future work.
展开▼
