Computing multicast trees in dynamic networks and the complexity of connected components in evolving graphs

Abstract

Future Internet technologies and the deployment of mobile and nomadic services enable complex communications networks that have a highly dynamic behavior. This naturally engenders route-discovery problems under changing conditions over these networks, but the temporal variations in the topology of dynamic networks are not effectively captured in a classical graph model. In this paper, we use evolving graphs, which help capture the dynamic characteristics of such networks, in order to compute multicast trees with minimum overall transmission time for a class of wireless mobile dynamic networks. We first show that computing different types of strongly connected components in evolving digraphs is NP-Hard, and then propose a polynomial-time algorithm to build all rooted directed Minimum Spanning Trees in strongly connected dynamic networks. These results open new avenues for the implementation of Internet spanning-tree based protocols over highly dynamic network infrastructures. © The Brazilian Computer Society 2012.