Alain Cournier

Enabling snap-stabilization

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]).

Self-stabilizing PIF algorithm in arbitrary rooted networks

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.

Snap-stabilizing PIF algorithm in arbitrary networks

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.

Snap-stabilizing PIF and useless computations

A snap-stabilizing protocol, starting from any configuration, always behaves according to its specification. In other words, a snap-stabilizing protocol is a self-stabilizing protocol which stabilizes in 0 time unit. Here, we propose the first snap-stabilizing propagation of information with feedback for arbitrary networks working with an unfair daemon. An interesting aspect of our solution is that, starting from any configuration, the number of reception (resp. acknowledgement) of corrupted messages (i.e., messages not initiated by the root) by a processor is bounded

An improved snap-stabilizing PIF algorithm

A snap-stabilizing protocol, starting from any arbitrary initial configuration, always behaves according to its specification. In [10], Cournier and al. present the first snap-stabilizing Propagation of Information with Feedback (PIF) protocol in arbitrary networks. But, in order to achieve the desirable property of snap-stabilization, the algorithm needs the knowledge of the exact size of the network. This drawback prevents the protocol from working on dynamical systems. In this paper, we propose an original protocol which solves this drawback.

The first fully polynomial stabilizing algorithm for BFS tree construction

The construction of a spanning tree is a fundamental task in distributed systems which allows to resolve other tasks (i.e., routing, mutual exclusion, network reset). In this paper, we are interested in the problem of constructing a Breadth First Search (BFS) tree. Stabilization is a versatile technique which ensures that the system recover a correct behavior from an arbitrary global state resulting from transient faults. A fully polynomial algorithm has a round complexity in O(da) and a step complexity in O(nb) where d and n are the diameter and the number of nodes of the network and a and b are constants. We present the first fully polynomial stabilizing algorithm constructing a BFS tree under a distributed daemon. Moreover, as far as we know, it is also the first fully polynomial stabilizing algorithm for spanning tree construction. Its round complexity is in O(d2) and its step complexity is in O(n6). To our knowledge, since in general the diameter of a network is much smaller than the number of nodes (log(n) in average instead of n), this algorithm reaches the best compromise of the literature between the complexities in terms of rounds and in terms of steps.

A snap-stabilizing DFS with a lower space requirement

A snap-stabilizing protocol, starting from any arbitrary initial configuration, always behaves according to its specification. In [4], we presented the first snap-stabilizing depth-first search (DFS) wave protocol for arbitrary rooted networks working under an unfair daemon. However, this protocol needs O(NN) states per processors (where N is the number of processors) and needs ids on processors. In this paper, we propose an original snap-stabilizing solution for this problem with a strongly enhanced space complexity, i.e., O(Δ2 × N) states where Δ is the degree of the network. Furthermore, this new protocol does not need a completely identified network: only the root needs to be identified, i.e., the network is semi-anonymous.

A snap-stabilizing point-to-point communication protocol in message-switched networks

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.

From self- to snap- stabilization

A snap-stabilizing protocol, starting from any configuration, always behaves according to its specification. In this paper, we propose a light semi-automatic method allowing to snap-stabilize self-stabilizing wave protocols for arbitrary networks with a unique initiator. To that goal, we consider such a self-stabilizing protocol A. We then slightly update A to obtain a protocol B that can be automatically transformed, using a black box protocol, into a snap-stabilizing protocol. B is easy to obtain from A compared to the design of a snap-stabilizing protocol.

How to Improve Snap-Stabilizing Point-to-Point Communication Space Complexity?

A snap-stabilizing protocol, starting from any configuration, always behaves according to its specification. In this paper, we are interested in 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 information given by a routing algorithm. By the context of stabilization (in particular, the system starts in any configuration), this information can be corrupted. In [1], authors show that there exists snap-stabilizing algorithms for this problem (in the state model ). That implies that we can ask the system to begin forwarding messages without losses even if routing informations are initially corrupted. In this paper, we propose another snap-stabilizing algorithm for this problem which improves the space complexity of the one of [1].