Stéphane Devismes

Optimal grid exploration by asynchronous oblivious robots

We consider deterministic terminating exploration of a grid by a team of asynchronous oblivious robots. We first consider the semi-synchronous atomic model ATOM. In this model, we exhibit the minimal number of robots to solve the problem w.r.t. the size of the grid. We then consider the asynchronous non-atomic model CORDA. ATOM being strictly stronger than CORDA, the previous bounds also hold in CORDA, and we propose deterministic algorithms in CORDA that matches these bounds. The above results show that except in two particular cases, 3 robots are necessary and sufficient to deterministically explore a grid of at least three nodes. The optimal number of robots for the two remaining cases is: 4 for the (2,2)-Grid and 5 for the (3,3)-Grid, respectively.

Self-Stabilizing Small k-Dominating Sets

A self-stabilizing algorithm, after transient faults hit the system and place it in some arbitrary global state, recovers in finite time without external (e.g., human) intervention. In this paper, we propose a distributed asynchronous silent self-stabilizing algorithm for finding a minimal k-dominating set of at most n/(k+1) processes in an arbitrary identified network of size n. We propose a transformer that allows our algorithm work under an unfair daemon (the weakest scheduling assumption). The complexity of our solution is in O(n) rounds and O(D n²) steps using O(log n + k log n) bits per process where D is the diameter of the network.

Optimal probabilistic ring exploration by semi-synchronous oblivious robots

We consider a team of k identical, oblivious, semi-synchronous mobile robots that are able to sense (i.e., view) their environment, yet are unable to communicate, and evolve on a constrained path. Previous results in this weak scenario show that initial symmetry yields high lower bounds when problems are to be solved by deterministic robots. In this paper, we initiate research on probabilistic bounds and solutions in this context, and focus on the exploration problem of anonymous unoriented rings of any size. It is known that Θ(logn) robots are necessary and sufficient to solve the problem with k deterministic robots, provided that k and n are coprime. By contrast, we show that four identical probabilistic robots are necessary and sufficient to solve the same problem, also removing the coprime constraint. Our positive results are constructive.

A Self-Stabilizing O(n)-Round k-Clustering Algorithm

Given an arbitrary network

Robust stabilizing leader election

G

Snap-stabilizing PIF and useless computations

of {\ndes} with unique IDs and no designated leader,and given a

Light enabling snap-stabilization of fundamental protocols

k

Communication Efficiency in Self-Stabilizing Silent Protocols

-dominating set

Snap-Stabilizing Depth-First Search on Arbitrary Networks

I\subseteq G

A snap-stabilizing DFS with a lower space requirement

, we propose a silent self-stabilizing distributed algorithm that computes a subset