Message Multicasting in Heterogeneous Networks

In heterogeneous networks, sending messages may incur different delays on different links, and each node may have a different switching time between messages. The well-studied telephone model is obtained when all link delays and switching times are equal to one unit. We investigate the problem of finding the minimum time required to multicast a message from one source to a subset of the nodes of size k. The problem is NP-hard even in the basic telephone model. We present a polynomial-time algorithm that approximates the minimum multicast time within a factor of O(log k). Our algorithm improves on the best known approximation factor for the telephone model by a factor of $O(\frac{\log n}{\log\log k})$. No approximation algorithms were known for the general model considered in this paper.