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We examine the problem of broadcasting in a point-to-point computer network where a message, originated by one node, is transmitted to all nodes, subject to the restriction that an informed node can call only one of its neighbors Auring a given time unit. A dynamic programming formulation for optimal broadcasting in general networks is given, and an exact algorithm based on it is developed. Since this algorithm is not very efficient for larger networks, we present a number of heuristics for achieving efficient near-optimal algorithms. In particular, we discuss in detail a class of heuristics which require finding at each step a least-weight maximum matching in a bipartite graph.