Gomory-Hu Trees Over Wireless

The Gomory-Hu tree is a popular optimization algorithm that enables to efficiently find a min-cut (or equivalently, max-flow) for every pair of nodes in a graph. However, graphs cannot capture broadcasting and interference in wireless: over wireless networks we need to resort to the information-theoretical cut-set to bound the max-flow. Leveraging the submodularity of mutual information, we show that the Gomory-Hu algorithm can be used to efficiently find information-theoretic rate characterizations such as the capacity or an approximation to the capacity, over a number of network scenarios including wireless Gaussian networks and deterministic relay networks.