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Rai et al. in [1] showed that any rational number p/q is the capacity of some sum-network. The authors proved this result by constructing such sum-networks. The authors first constructed a sum-network with capacity 1/q, and then they connected p of such networks in parallel to create a sum-network of capacity p/q. Such construction requires 2q2 - q number of sources and 2q2-q number of terminals....
In this paper, we consider sum-networks, which is a class of directed acyclic networks where each terminal in the network requires sum of all the sources. In the literature, all reported sum-networks are shown to have only certain rational valued coding capacities. For example, it has been shown that a sum-network, having 3 sources and 3 terminals, has coding capacity either 0, 2 over 3 or ≥ 1. It...
In this paper, we consider sum-networks where each terminal requires sum of all the sources. For a sum-network having 3 sources and 3 terminals, it is known that the network is solvable if the min-cut between each source and each terminal is at least 2. However, it is not known whether this condition is sufficient for sum-networks having arbitrary number of sources and terminals. In the present work,...
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