Proceedings ArticleDOI
On the Generalized Network Sharing bound and edge-cut bounds for network coding
Sudeep Kamath,David Tse +1 more
- pp 2735-2739
TLDR
It is shown that the Generalized Network Sharing bound is equivalent to a functional dependence bound in the literature and the problem of computing the GNS bound is NP-complete, even for two-unicast networks.Abstract:
We consider sum-rate edge-cut bounds on network coding rates for the multiple unicast problem. We first show that the Generalized Network Sharing (GNS) bound is equivalent to a functional dependence bound in the literature. After defining a notion of profile of an edge-cut, we show that the only profiles for which, every edge-cut with the said profile leads to a fundamental bound on network coding rates, are the so-called GNS profiles and further, we quantify with a tight constant factor, the amount by which network coding can potentially beat edge-cuts associated with other profiles. Finally, we show that the problem of computing the GNS bound is NP-complete, even for two-unicast networks.read more
Citations
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A study of some problems in network information theory
TL;DR: This dissertation suggests that a significant aspect of the difficulty in studying limits of communication over networks lies in the unidirectional aspects of the problem, and finds that simple schemes are approximately optimal in achieving these fundamental limits.
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Random threshold graphs with exponential fitness: The width of the phase transition for connectivity
Armand M. Makowski,Osman Yaggan +1 more
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Linear Network Coding for Two-Unicast-$Z$ Networks: A Commutative Algebraic Perspective and Fundamental Limits
Mohammad Fahim,Viveck R. Cadambe +1 more
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References
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