No abstract

In this article, we show that some fundamental self-and snap-stabilizing wave protocols (e.g., token circulation, PIF, etc.) implicitly assume a very light property that we call BreakingIn. We prove that BreakingIn is strictly induced by self-and snap-stabilization. Combined with a transformer, BreakingIn allows to easily turn the non-fault-tolerant versions of those protocols into snap-stabilizing versions. Unlike the previous solutions, the transformed protocols are very efficient and work at least with the same daemon as the initial versions extended to satisfy BreakingIn. Finally, we show how to use an additional property of the transformer to design snap-stabilizing extensions of those fundamental protocols like Mutual Exclusion.

No abstract

No abstract

No abstract

No abstract

Abstract.A snap-stabilizing protocol, starting from any arbitrary initial configuration, always behaves according to its specification. In this paper, we present a snap-stabilizing depth-first search wave protocol for arbitrary rooted networks. In this protocol, a wave of computation is initiated by the root. In this wave, all the processors are sequentially visited in depth-first search order. After the end of the visit, the root eventually detects the termination of the process. Furthermore, our protocol is proven assuming an unfair daemon, i.e., assuming the weakest scheduling assumption.

We propose a silent self-stabilizing leader election algorithm for bidirectional arbitrary connected identified networks. This algorithm is written in the locally shared memory model under the distributed unfair daemon. It requires no global knowledge on the network. Its stabilization time is in Θ(n 3) steps in the worst case, where n is the number of processes. Its memory requirement is asymptotically optimal, i.e., Θ(log n) bits per processes. Its round complexity is of the same order of magnitude-i.e., Θ(n) rounds-as the best existing algorithms designed with similar settings. To the best of our knowledge, this is the first self-stabilizing leader election algorithm for arbitrary identified networks that is proven to achieve a stabilization time polynomial in steps. By contrast, we show that the previous best existing algorithms designed with similar settings stabilize in a non polynomial number of steps in the worst case.