Stabilization of Routing in Directed Networks

Routing messages in a network is often based on the assumption that each link, and so each path, in the network is bidirectional. The two directions of a path are employed in routing messages as follows. One direction is used by the nodes in the path to forward messages to their destination at the end of the path, and the other direction is used by the destination to inform the nodes in the path that this path does lead to the destination. Clearly, routing messages is more difficult in directed networks where links are unidirectional. (Examples of such networks are mobile ad-hoc networks and satellite networks.) In this paper, we present the first stabilizing protocol for routing messages in directed networks. We keep our presentation manageable by dividing it into three (relatively simple) steps. In the first step, we develop an arbitrary directed network where each node broadcasts to every reachable node in the network. In the second step, we enhance the network such that each node broadcasts its shortest distance to the destination. In the third step, we enhance the network further such that each node can determine its best neighbor for reaching the destination.