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(da) and a step complexity in O(nb) 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 Θ(d2) and its step complexity is in O(n6).
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