Minimum Gossip Digraphs

Gossiping is a problem of information dissemination described in a group of individuals connected by a communication network, where every individual in the network knows a unique item of information and needs to communicate it to everyone else. This communication pattern nds its main applications in the eld of interconnection networks for parallel and distributed architecture. Previous papers have investigated ways to construct sparse graphs (networks) in which this process can be completed in minimum time. In this paper, we consider the gossiping problem in directed graphs. We discuss about the minimum time necessary to achieve gossiping in digraphs, and describe several techniques to construct sparse digraphs on n vertices in which gossiping can be completed in minimum time. For some small values of n (1 n 8), these techniques produce the sparsest possible digraphs of this type (called minimum gossip digraphs). For other values of n, these techniques produce the sparsest known digraphs of this type.