Disconnected components detection and rooted shortest-path tree maintenance in networks - extended version

Overview & Synopsis

Many articles deal with the problem of maintaining a rooted shortest-path tree. However , after some edge deletions, some nodes can be disconnected from the connected component V r of some distinguished node r. In this case, an additional objective is to ensure the detection of the disconnection by the nodes that no longer belong to V r. We present a detailed analysis of a silent self-stabilizing algorithm. We prove that it solves this more demanding task in anonymous networks with the following properties: it runs without any knowledge on the network and under the unfair daemon, that is without any assumption on the asynchronous model. Moreover, it terminates in less than 2n + D rounds for a network of n nodes and hop-diameter D.