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Some generalized communication modes enabling the dissemination of information among processors of interconnection networks via vertex-disjoint or edge-disjoint paths in one communication step will be investigated. A thorough study of these communication modes will be presented by giving optimal algorithms for broadcasting, accwnulatian and gossiping in most of the well-known parallel architectures. For those networks in which a Hamiltonian path exists (hypercubes, cube connected cycles,doi:10.1016/0166-218x(94)90179-1 fatcat:yic5npkmdnbyfir27f3cslumzm