Two-unicast is hard

@article{Kamath2014TwounicastIH,
  title={Two-unicast is hard},
  author={Sudeep Kamath and David Tse and Chih-Chun Wang},
  journal={2014 IEEE International Symposium on Information Theory},
  year={2014},
  pages={2147-2151}
}
Consider the k-unicast network coding problem over an acyclic wireline network: Given a rate vector k-tuple, determine whether the network of interest can support k unicast flows with those rates. It is well known that the one-unicast problem is easy and that it is solved by the celebrated max-flow min-cut theorem. The hardness of k-unicast problems with small k has been an open problem. We show that the two-unicast problem is as hard as any k-unicast problem for k ≥ 3. Our result suggests that… CONTINUE READING
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References

Publications referenced by this paper.
Showing 1-10 of 15 references

Networks, Matroids, and Non-Shannon Information Inequalities

IEEE Transactions on Information Theory • 2007
View 5 Excerpts
Highly Influenced

Insufficiency of linear coding in network information flow

IEEE Transactions on Information Theory • 2005
View 6 Excerpts
Highly Influenced

An Edge Reduction Lemma for linear network coding and an application to two-unicast networks

2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton) • 2012

A Note on the Multiple Unicast Capacity of Directed Acyclic Networks

2011 IEEE International Conference on Communications (ICC) • 2011
View 1 Excerpt

Generalized Network Sharing Outer Bound and the Two-Unicast Problem

2011 International Symposium on Networking Coding • 2011
View 1 Excerpt

Multi-Commodity Network Flows over Multipaths with Bounded Buffers

2010 IEEE International Conference on Communications • 2010
View 1 Excerpt

Pairwise Intersession Network Coding on Directed Networks

IEEE Transactions on Information Theory • 2010
View 2 Excerpts

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