Mathematical Methods of Operations Research

, Volume 77, Issue 3, pp 381–391

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

Original Article

## Abstract

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 ki 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 ki 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 (k1, k2)-splittable flow without chunk size restrictions for fixed demand ratios.

### Keywords

Splittable flow 2-commodity flow Approximation algorithm

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### References

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