Snap-Stabilizing PIF on Non-oriented Trees and Message Passing Model

Abstract

AbstractStarting from any configuration, a snap-stabilizing protocol guarantees that the system always behaves according to its specification while a self-stabilizing protocol only guarantees that the system will behave according to its specification in a finite time. So, a snap-stabilizing protocol is a time optimal self-stabilizing protocol (because it stabilizes in 0 rounds). That property is very suitable in the case of systems that are prone to transient faults. There exist a lot of approaches of the concept of self-stabilization, but to our knowledge, snap-stabilization is the only variant of self-stabilization which has been proved power equivalent to self-stabilization in the context of the state model (a locally shared memory model) and for non anonymous systems. So the problem of the existence of snap-stabilizing solutions in the message passing model is a very crucial question from a practical point of view. In this paper, we present the first snap-stabilizing propagation of information with feedback (PIF) protocol for non-oriented trees in the message passing model. Moreover using slow and fast timers, the round complexity of our algorithm is in θ(h ×k) and θ((h ×k) + k 2), respectively, where h is the height of the tree and k is the maximal capacity of the channels. We conjecture that our algorithm is optimal.KeywordsFast TimerBroadcast MessageTransient FaultInternal ProcShare Memory ModelThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.