Optimal algorithms for dissemination of information in generalized communication modes

Abstract

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 are investigated. A thorough study of these communication modes is presented by giving optimal algorithms for broadcasting, accumulation and gossiping in most of the well known parallel architectures. For those networks in which a hamiltonian path exists (hypercubes, cube connected cycles, butterflies, etc.), optimal algorithms are obtained quite easily. But for complete binary trees, complete k-ary trees (k≥3) and arbitrary k-degree bounded graphs, the optimal algorithms as well as the matching lower bound proofs are more involved. An interesting consequence of the presented algorithms is the fact that in almost all these interconnection networks the gossip problem cannot be solved in time less than the sum of time complexities of the accumulation problem and the broadcast problem (i.e. for most networks the optimal algorithm for the gossip problem is simply the concatenation of optimal algorithms for accumulation and broadcasting).