# The First Fully Polynomial Stabilizing Algorithm for BFS Tree Construction

2 CEDRIC - ROC - CEDRIC. Réseaux et Objets Connectés
CEDRIC - Centre d'études et de recherche en informatique et communications
Abstract : 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 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 $O(n^6)$.
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Journal articles

https://hal.archives-ouvertes.fr/hal-02470990
Contributor : Stephane Rovedakis <>
Submitted on : Friday, February 7, 2020 - 4:29:25 PM
Last modification on : Wednesday, February 19, 2020 - 12:57:54 PM

### Citation

Alain Cournier, Stephane Rovedakis, Vincent Villain. The First Fully Polynomial Stabilizing Algorithm for BFS Tree Construction. Information and Computation, Elsevier, 2019, 265, pp.26-56. ⟨10.1016/j.ic.2019.01.005⟩. ⟨hal-02470990⟩

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