Optimal odd gossiping

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Optimal odd gossiping

In the gossiping problem, each node of a network starts with a unique piece of information and must acquire the information of all the other nodes. This is done using two-way communications between pairs of nodes. In this paper, we consider gossiping in n-node networks with n odd, where we use a linear cost model, in which the cost of communication is proportional to the amount of information transmitted. We also assume a synchronous model, in which the pairwise communications are organized into rounds, and all communications in one round start at the same time. Each communication between two vertices during a given round uses a certain number of steps, each step being the time to exchange an indivisible piece of information. Fertin and Peters [3] have given optimal gossip algorithms in the synchronous model for odd n when Rn, the number of rounds, is minimum (Rn=dlog 2(n)e+1) ; that is, they have determined the minimum number of steps Sn that are used in a synchronous gossip algorithm withdlog2(n)e+1 rounds. As suggested in [4] and [3], we study in this paper the trade-offs between Rn and Sn for odd n in the linear cost model in the synchronous case. We show several bounds on Sn (resp. on Rn) when the optimality condition on Rn (resp. Sn) is relaxed. We show that some of these bounds are tight for an infinite number of cases, and discuss such results

Optimal Odd Gossiping

In the gossiping problem, each node in a network starts with a unique piece of information and must acquire the information of all other nodes using two-way communications between pairs of nodes. In this paper we investigate gossiping in n-node networks with n odd. We use a linear cost model in which the cost of communication is proportional to the amount of information transmitted. In synchronous gossiping, the pairwise communications are organized into rounds, and all communications in a round start at the same time. We present optimal synchronous algorithms for all odd values of n. In asynchronous gossiping, a pair of nodes can start communicating while communications between other pairs are in progress. We provide a short intuitive proof that an asynchronous lower bound due to Peters, Raabe, and Xu is not tight