# [CRV19] The First Fully Polynomial Stabilizing Algorithm for BFS Tree

Revue Internationale avec comité de lecture : Journal Information and Computation, vol. 265, pp. 26-56, 2019, (doi:https://doi.org/10.1016/j.ic.2019.01.005)

Mots clés: Distributed systems, Fault-tolerance, Stabilization, Spanning tree construction

Résumé: 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 recovers a correct behavior from an arbitrary global state resulting from transient faults. A \emph{fully polynomial} algorithm has a round complexity in $O(d^a)$ and a step complexity in $O(n^b)$ 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 $\Theta(d^2)$ and its step complexity is in $O(n^6)$.

Collaboration: Laboratoire MIS

# BibTeX

 @article { CRV19, title = "{The First Fully Polynomial Stabilizing Algorithm for BFS Tree}", author = "A. Cournier and S. Rovedakis and V. Villain", journal = "Information and Computation", year = 2019, volume = 265, pages = "26-56", doi = "https://doi.org/10.1016/j.ic.2019.01.005", }