Mathematical Methods of Operations Research

, Volume 77, Issue 3, pp 381–391 | Cite as

A polynomial time approximation algorithm for the two-commodity splittable flow problem

  • Elke Eisenschmidt
  • Utz-Uwe Haus
Original Article


We consider a generalization of the unsplittable maximum two-commodity flow problem on undirected graphs where each commodity \({i \in \{1, 2\}}\) can be split into a bounded number k i of equally-sized chunks that can be routed on different paths. We show that in contrast to the single-commodity case this problem is NP-hard, and hard to approximate to within a factor of α > 1/2. We present a polynomial time 1/2-approximation algorithm for the case of uniform chunk size over both commodities and show that for even k i and a mild cut condition it can be modified to yield an exact method. The uniform case can be used to derive a 1/4-approximation for the maximum concurrent (k 1, k 2)-splittable flow without chunk size restrictions for fixed demand ratios.


Splittable flow 2-commodity flow Approximation algorithm 


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Institut für Mathematische OptimierungOtto-von-Guericke Universität MagdeburgMagdeburgGermany
  2. 2.Institut für Operations ResearchETH ZürichZurichSwitzerland

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