Self-Stabilizing PIF Algorithm in Arbitrary Rooted Networks

We present a deterministic distributed Propagation of Information with Feedback (PIF) protocol in arbitrary rooted networks. The proposed algorithm does not use a preconstructed spanning tree. The protocol is self-stabilizing, meaning that starting from an arbitrary state (in response to an arbitrary perturbation modifying the memory state), it is guaranteed to behave according to its specification. Every PIF wave initiated by the root inherently creates a tree in the graph. So, the tree is dynamically created according to the progress of the PIF wave. This allows our PIF algorithm to take advantage of the relative speed of different components of the network. The proposed algorithm can be easily used to implement any self-stabilizing system which requires a (self-stabilizing) wave protocol running on an arbitrary network.