Gossiping and broadcasting are two problems of information dissemination described for a group of individuals connected by a communication network. In gossiping every person in the network knows a unique item of information and needs to communicate it to everyone else. In broadcasting one individual has an item of information which needs to be communicated to everyone else. We review the results that have been obtained on these and related problems.

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A spanning subgraph S = (V, E') of a connected simple graph G = (V, E ) is a f(x)-spanner if for any pair of nodes u and v, ds(u, v) 5 f(d& v)), where do and ds are the usual distance functions in graphs G and S, respectively. We are primarily interested in (t + x)-spanners, which we refer to as additive spanners. We construct low-degree additive spanners for X-trees, pyramids, and multidimensional grids. We prove, for arbitrary t > 0, that to determine whether a given graph G has an additive spanner with no more than m edges is NP-complete. 0 1993 by John Wiley & Sons, Inc.