Abstract
We propose two self-stabilizing algorithms for tree networks. The first one computes a special label, called guide pair of each process P in O(h) rounds (h being the height of the tree) using O(δ P logn) space per process P, where δ P is the degree of P and n the number of processes in the network. Guide pairs have numerous applications, including ordered traversal or navigation of the processes in the tree. Our second self-stabilizing algorithm, which uses the guide pairs computed by the first algorithm, solves the ranking problem in O(n) rounds and has space complexity O(b + δ P logn) in each process P, where b is the number of bits needed to store a value. The first algorithm orders the tree processes according to their topological positions. The second algorithm orders (ranks) the processes according to the values stored in them.
This work has been partially supported by the ANR project ARESA2.
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Datta, A.K., Devismes, S., Larmore, L.L., Rivierre, Y. (2011). Self-stabilizing Labeling and Ranking in Ordered Trees. In: Défago, X., Petit, F., Villain, V. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2011. Lecture Notes in Computer Science, vol 6976. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24550-3_13
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DOI: https://doi.org/10.1007/978-3-642-24550-3_13
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