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 recover 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 O(d 2) and its step complexity is in O(n 6).
To our knowledge, since in general the diameter of a network is much smaller than the number of nodes (log(n) in average instead of n), this algorithm reaches the best compromise of the literature between the complexities in terms of rounds and in terms of steps.
This work has been supported in part by the ANR project SPADES (08-ANR-SEGI-025).
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Cournier, A., Rovedakis, S., Villain, V. (2011). The First Fully Polynomial Stabilizing Algorithm for BFS Tree Construction. In: Fernàndez Anta, A., Lipari, G., Roy, M. (eds) Principles of Distributed Systems. OPODIS 2011. Lecture Notes in Computer Science, vol 7109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25873-2_12
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