Self-stabilizing Systems in Spite of High Dynamics

Abstract

We initiate research on self-stabilization in highly dynamic identified message passing systems where dynamics is modeled using time-varying graphs (TVGs). More precisely, we address the self-stabilizing leader election problem in three wide classes of TVGs: the class of TVGs with temporal diameter bounded by Δ, the class of TVGs with temporal diameter quasi-bounded by Δ, and the class of TVGs with recurrent connectivity only, where . We first study conditions under which our problem can be solved. We introduce the notion of size-ambiguity to show that the assumption on the knowledge of the number n of processes is central. Our results reveal that, despite the existence of unique process identifiers, any deterministic self-stabilizing leader election algorithm working in the class or cannot be size-ambiguous, justifying why our solutions for those classes assume the exact knowledge of n. We then present three self-stabilizing leader election algorithms for Classes , , and , respectively. Our algorithm for stabilizes in at most 3Δ rounds. In and , stabilization time cannot be bounded, except for trivial specifications. However, we show that our solutions are speculative in the sense that their stabilization time in is O(Δ) rounds.