Note on Optimal Gossiping in Some Weak-Connected Graphs

The problems of gossiping and broadcasting in one-way communication mode are investigated. Optimal algorithms for gossip problem are known only for the complete graphs, paths, some simple trees, and cycles. In this paper some lower bounds on gossiping in graphs with bridges or with edge disjoint cycles are proved. A direct consequence of these lower bounds are optimal gossip algorithms for some families of weak-connected graphs. Another question considered here is the relation between the gossip problem and the broadcast problem. Gossiping cannot be harder than two times broadcasting, and only for trees it is known that gossiping is exactly two times harder than broadcasting. Using the above mentioned lower bounds some other graphs (having cycles) with this property are found.