Snap-Stabilizing PIF on Arbitrary Connected Networks in Message Passing Model
Starting from any configuration, a snap-stabilizing algorithm guarantees that the system always behaves according to its specification while a self-stabilizing algorithm only guarantees that the system will behave according to its specification in a finite time. So, a snap-stabilizing algorithm is a time optimal self-stabilizing algorithm (because it stabilizes in 0 rounds). That means that even the first attempt of using a snap-stabilizing algorithm by any user (human or algorithm) will produce a correct execution. This is a very desirable property, especially in the case of systems that are prone to transient faults. 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.