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STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Preserving and Increasing Local Edge-Connectivity in Mixed Graphs
SIAM Journal on Discrete Mathematics
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Polynomial time algorithms for network information flow
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
An algebraic approach to network coding
IEEE/ACM Transactions on Networking (TON)
Deterministic network coding by matrix completion
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
ICUFN'09 Proceedings of the first international conference on Ubiquitous and future networks
Perfect secrecy, perfect omniscience and steiner tree packing
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Perfect omniscience, perfect secrecy, and Steiner tree packing
IEEE Transactions on Information Theory
Rate control with pairwise intersession network coding
IEEE/ACM Transactions on Networking (TON)
HAIS'11 Proceedings of the 6th international conference on Hybrid artificial intelligent systems - Volume Part I
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Given a network of lossless links with rate constraints, a source node, and a set of destination nodes, the multicast capacity is the maximum rate at which the source can transfer common information to the destinations. The multicast capacity cannot exceed the capacity of any cut separating the source from a destination; the minimum of the cut capacities is called the cut bound. A fundamental theorem in graph theory by Edmonds established that if all nodes other than the source are destinations, the cut bound can be achieved by routing. In general, however, the cut bound cannot be achieved by routing. Ahlswede et al. established that the cut bound can be achieved by performing network coding, which generalizes routing by allowing information to be mixed. This paper presents a unifying theorem that includes Edmonds' theorem and Ahlswede et al.'s theorem as special cases. Specifically, it shows that the multicast capacity can still be achieved even if information mixing is only allowed on edges entering relay nodes. This unifying theorem is established via a graph theoretic hardwiring theorem, together with the network coding theorems for multicasting. The proof of the hardwiring theorem implies a new proof of Edmonds' theorem.