# Gossiping in vertex-disjoint paths mode in interconnection networks

## Abstract

- 1.
Optimal gossip algorithms for paths, complete graphs and flakes in both modes.

- 2.
For hypercubes, cube-connected cycles, butterfly networks, etc., gossip algorithms which are only about

*O*(log_{2}log_{2}*n*) rounds slower than the optimal gossip algorithms on complete graphs are designed. Furthermore, it is shown that at least Ω(log_{2}log_{2}log_{2}*n*) rounds more than needed by the optimal gossip algorithm on the complete graph are necessary for every “well-structured” gossip algorithm on networks with “small” degree.

Note that the results achieved have also practical application, because the vertex-disjoint paths mode can be implemented in several hardware realisations of computing networks.

## Keywords

Complete Graph Interconnection Network Hamiltonian Path Communication Step Permutation Network## Preview

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