On the capacity of ms/3t and 3s/nt sum-networks

摘要: We consider directed acyclic networks where each terminal requires sum of all the sources. Such a class has been termed as sum-networks in literature. A sum-network having m sources and n terminals ms/nt sum-network. There previous works on capacity sum-networks, specifically, it shown that 3s/3t is either 0,2/3 or ≥ 1. In this paper, we some generalizations namely, ms/3t 3s/nt m, 3. For 3, if mincut between source at least 1, known to be 2/3. show there exist whose capacities lie 2/3 Specifically, for any positive integer k 2, exists (and also sum-network) k/k+1. conjecture sum-network, > 3 3) 0, 1 form k/k+1, greater than equal 2.