Stabilization of Loop-Free Redundant Routing

Consider a network of processes that exchange messages via FIFO communication channels. Each process chooses a subset of its neighboring processes to be its successors. Furthermore, there is a distinguished process, called root, that may be reached from any other process by following the successor relation at each hop. Thus, under the successor relation, the processes are arranged as a directed acyclic graph that converges on the root process, i.e., a converging DAG (c-DAG). We present a network where each process may dynamically change its choice of successors, and during this change, the following two nice properties are satisfied. First, if the initial state of the network forms a c-DAG, then a c-DAG is preserved at all times. Second, if the protocol is started from an arbitrary state (i.e., where each variable has an arbitrary value), then a c-DAG is automatically restored.