An improved stabilizing BFS tree construction

Alain Cournier (1) , Stephane Rovedakis (2) , Vincent Villain (1)

1 MIS - Modélisation, Information et Systèmes - UR UPJV 4290
2 CEDRIC - Centre d'études et de recherche en informatique et communications

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 \emph{Breadth First Search} (BFS) tree. \emph{Stabilization} is a versatile technique which ensures that the system recover a correct behaviour from an arbitrary global state resulting from transient faults. A \emph{silent} algorithm always reaches a terminal global state in a finite time. We present a first silent stabilizing algorithm to resolve a problem in which each node requests a permission (delivered by a subset of network nodes) in order to perform a defined computation. Using this first algorithm, we present a silent stabilizing algorithm constructing a BFS tree working in $O(D^2)$ rounds ($D$ is the diameter of the network) under a distributed daemon without any fairness assumptions. The complexity in terms of steps is $O(mn^4)$ where $m$ and $n$ are the number of edges and nodes of the network, respectively, so it is polynomial with respect to $n$. To our knowledge, since in general the diameter of a network is much smaller than the number of nodes, this algorithm gets the best compromise of the literature between the complexities in terms of rounds and in terms of steps.

Mots clés: Distributed algorithm; Fault-tolerance; Self-stabilization; Spanning tree construction

Domaines: Calcul parallèle, distribué et partagé [cs.DC]; Réseaux et télécommunications [cs.NI]

Alain Cournier, Stephane Rovedakis, Vincent Villain. An improved stabilizing BFS tree construction. 2011. ⟨hal-00589950⟩