Broadcasting in Heterogeneous Tree Networks

We consider the broadcasting problem in heterogeneous tree networks. A heterogeneous tree network is represented by a weighted tree T = (V, E) such that the weight of each edge denotes the communication time between the two end vertices. The broadcasting problem is to find a broadcast center such that the maximum communication time from the broadcast center to all vertices is minimized. In this paper, we propose a linear time algorithm for the broadcasting problem in a heterogeneous tree network following the postal model. As a byproduct of the algorithm, we can compute in linear time the broadcasting time of any vertex in the tree, i.e., the maximum time required to transmit messages from the vertex to every other vertex in the tree. Furthermore, an optimal sequence by which the broadcast center broadcasts its messages to all vertices in T can also be determined in linear time.