We consider identified directed networks where processes know an upper bound on the maximum ancestor distance. Under these settings, we study the conditions on the network topology allowing the self-stabilization of two fundamental problems: the leader election and the synchronous unison. We show that those two problems can be self-stabilizingly solved in our settings if and only if the network contains a unique source component. In particular, to show that our condition is sufficient, we propose two algorithms and study their complexity. Notice that our topological condition covers a wide spectrum of digraphs since, for example, strongly connected digraphs, dipaths, and out-trees have a unique source component.

Self-stabilization is a general paradigm that characterizes the ability of a distributed system to recover from transient faults. Since its introduction by Dijkstra in 1974, self-stabilization has been successfully applied to efficiently solve many networking tasks. However, most of the literature focuses on bidirectional networks. Now, in today's networks such as WSNs, some communication channels may be one-way only. Considering such network topologies, a.k.a. directed graphs, makes self-stabilization more complicated, and sometimes even impossible. In this paper, we investigate the gap in terms of requirements and efficiency when considering a directed graph instead of an undirected one as network topology for a self-stabilizing algorithm. Our case study is a variant of a synchronous unison algorithm proposed by Arora et al.; the synchronous unison being a clock synchronization problem.

A snap-stabilizing protocol, starting from any configuration, always behaves according to its specification. In this paper, we present a snap-stabilizing protocol to solve the message forwarding problem in a message-switched network. In this problem, we must manage resources of the system to deliver messages to any processor of the network. In this purpose, we use informations given by a routing algorithm. By the context of stabilization (in particular, the system starts in any configuration), these informations can be corrupted. So, the existence of a snap-stabilizing protocol for the message forwarding problem implies that we can ask the system to begin forwarding messages even if routing informations are initially corrupted. In this paper, we propose a snap-stabilizing algorithm (in the state model) for the following specification of the problem: Any message can be generated in a finite time. Any emitted message will be delivered to its destination once and only once in a finite time. This implies that our protocol can deliver any emitted message regardless of the state of routing tables in the initial configuration.

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.

A snap-stabilizing protocol, starting from any arbitrary initial configuration, always behaves according to its specification. In this paper, we present the first snap-stabilizing depth-first search wave protocol for arbitrary rooted networks assuming an unfair daemon, i.e. assuming the weakest scheduling assumption (a preliminary version of this work was presented in OPODIS 2004, 8th International Conference on Principles of Distributed Systems, Grenoble (France)).

A snap-stabilizing protocol guarantees that the system always behaves according to its specification provided some processor initiated the protocol. We present how to snap-stabilize some important protocols, like Leader Election, Reset, Snapshot, and Termination Detection. We use a Snap-stabilizing Propagation of Information with Feedback protocol for arbitrary networks as the key module in the above transformation process. Finally, we design a universal transformer to provide a snap-stabilizing version of any protocol (which can be self-stabilized with the transformer of [15]).

We present the first snap-stabilizing propagation of information with feedback (PIF) protocol in arbitrary networks. A snap-stabilizing protocol, starting from any arbitrary initial system configuration, always behaves according to its specification. Our protocol is distributed, deterministic, and does not use a pre-constructed spanning tree.

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.