The all-or-nothing flow problem in directed graphs with symmetric demand pairs

Chandra Chekuri, Alina Ene
2014 Mathematical programming  
We study the approximability of the All-or-Nothing multicommodity 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 1 t 1 , s 2 t 2 , . . . , s k t k }. A subset M of the pairs is routable if there is a feasible multicommodity flow in G such that, for each pair s i t 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
more » ... t 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 [11] 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.
doi:10.1007/s10107-014-0856-z fatcat:l4cjh42tf5evbeprkaikfqwlte