Effective Systolic Algorithms for Gossiping in Cycles and Two-Dimensional Grids (Extended Abstract)

The complexity of systolic dissemination of information in one-way (telegraph) and two-way (telephone) communication mode is investigated. The following main results are established: (i) tight lower and upper bounds on the complexity of one-way systolic gossip in cycles for any length of the systolic period, (ii) optimal one-way and two-way systolic gossip algorithms in 2-dimensional grids whose complexity (the number of rounds) meets the trivial lower bound (the sum of the sizes of its dimensions).

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