Optimal algorithms for dissemination of information in some interconnection networks

Abstract

The problems of gossiping and broadcasting in one-way communication mode are considered for some prominent families of graphs. The complexity is measured as the number of communication rounds in the gossip and broadcast algorithms. The main result of the paper is the precise estimation of the gossip-problem complexity in cycles. To obtain this result a new combinatorial analysis of gossiping in cycles is developed. This analysis leads to an optimal lower bound on the number of rounds, and also to the design of an optimal algorithm for gossiping in cycles. The optimal algorithm for gossiping is later used to design new, effective algorithms for gossiping in important families of interconnection networks (cube connected cycles, butterfly networks). Furthermore, a new, effective algorithm for broadcasting in shuffle-exchange networks is developed.