Stéphane Messika

Fault-tolerant and self-stabilizing mobile robots gathering

Gathering is a fundamental coordination problem in cooperative mobile robotics. In short, given a set of robots with arbitrary initial location and no initial agreement on a global coordinate system, gathering requires that all robots, following their algorithm, reach the exact same but not predetermined location. Gathering is particularly challenging in networks where robots are oblivious (i.e., stateless) and the direct communication is replaced by observations on their respective locations. Interestingly any algorithm that solves gathering with oblivious robots is inherently self-stabilizing. In this paper, we significantly extend the studies of deterministic gathering feasibility under different assumptions related to synchrony and faults (crash and Byzantine). Unlike prior work, we consider a larger set of scheduling strategies, such as bounded schedulers, and derive interesting lower bounds on these schedulers. In addition, we extend our study to the feasibility of probabilistic gathering in both fault-free and fault-prone environments. To the best of our knowledge our work is the first to address the gathering from a probabilistic point of view.

Self-stabilizing counting in mobile sensor networks

Distributed computing has to adapt its techniques to mobile sensor networks and cope with constraints like small memory size or lack of computation power. In this paper we extend the results of Angluin et al (see [1,2,3,4]) by finding self-stabilizing algorithms to count the number of agents in the network. We focus on two different models of communication, with a fixed antenna or with pairwise interactions. In both models we decide if there exist algorithms (probabilistic, deterministic, with k-fair adversary) to solve the self-stabilizing counting problem.

Brief announcement: computing automatically the stabilization time against the worst and the best schedules

In this paper, we reduce the problem of computing the convergence time for a randomized self-stabilizing algorithm to an instance of the stochastic shortest path problem (SSP). The solution gives us a way to compute automatically the stabilization time against the worst and the best policy. Moreover, a corollary of this reduction ensures that the best and the worst policy for this kind of algorithms are memoryless and deterministic. We apply these results here in a toy example. We just present here the main results, to more details, see [1].

All k-bounded policies are equivalent for self-stabilization

We reduce the problem of proving the convergence of a randomized self-stabilizing algorithm under k-bounded policies to the convergence of the same algorithm under a specific policy. As a consequence, all k-bounded schedules are equivalent: a given algorithm is self-stabilizing under one of them if and only if it is self-stabilizing under any of them.