Mathematical Programming

, Volume 154, Issue 1–2, pp 249–272 | Cite as

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

  • Chandra Chekuri
  • Alina EneEmail author
Full Length Paper Series B


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 \(\mathcal {M}= \left\{ s_1t_1, s_2t_2, \ldots , s_kt_k\right\} \). A subset \(\mathcal {M}'\) of the pairs is routable if there is a feasible multicommodity flow in \(G\) such that, for each pair \(s_it_i \in \mathcal {M}'\), 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 Chekuri et al. (2005) 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.

Mathematics Subject Classification



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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2014

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignChicagoUSA
  2. 2.Center for Computational IntractabilityPrinceton UniversityPrincetonUSA
  3. 3.Department of Computer Science and DIMAPUniversity of WarwickCoventryUK

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