The all-or-nothing multicommodity flow problem
Chandra Chekuri, Sanjeev Khanna, F. Bruce Shepherd · 2004
We consider the all-or-nothing multicommodity flow problem in general graphs. We are given a capacitated undirected graph G=(V,E,u) and set of k pairs s1t1, s2t2, …, sktk. Each pair has a unit demand. The objective is to find a largest subset S of 1,2,…,k such that for every i in S we can send a flow of one unit between si and ti. Note that this differs from the edge-disjoint path problem (EDP) in that we do not insist on integral flows for the pairs. This problem is NP-hard, and APX-hard, even on trees. For trees, a 2--approximation is known for the cardinality case and a 4--approximation for the weighted case. In this paper we build on a recent result of Racke on low congestion oblivious routing in undirected graphs to obtain a poly-logarithmic approximation for the all-or-nothing problem in general undirected graphs. The best previous known approximation for all-or-nothing flow problem was O(min(n