OPTIMAL-ALGORITHMS FOR DISSEMINATION OF INFORMATION IN GENERALIZED COMMUNICATION MODES

Some generalized communication modes enabling the dissemination of inf ormation among processors of interconnection networks via vertex-disjo int or edge-disjoint paths in one communication step will be investiga ted. A thorough study of these communication modes will be presented b y giving optimal algorithms for broadcasting, accumulation and gossipi ng in most of the well-known parallel architectures. For those network s in which a Hamiltonian path exists (hypercubes, cube connected cycle s, butterflies, shuffle exchange, etc.) optimal algorithms can be obta ined quite easily, but for complete binary trees, complete k-ary trees (k greater-than-or-equal-to 3) and arbitrary degree bounded graphs, t he optimal algorithms as well as the matching lower bound proofs are m ore involved. An interesting consequence of the presented algorithms i s the fact that in almost all these interconnection networks the gossi p problem cannot be solved in less time than the sum of time complexit ies of the accumulation problem and the broadcast problem (i.e. for mo st networks the optimal algorithm for the gossip problem is simply the concatenation of optimal algorithms for accumulation and broadcasting ).