Abstract
Resource Discovery is a crucial issue in the deployment of computational grids over large scale peer-to-peer platforms. Because they efficiently allow range queries, Tries (a.k.a., Prefix Trees) appear to be among promising ways in the design of distributed data structures indexing resources. Self-stabilization is an efficient approach in the design of reliable solutions for dynamic systems. A snap-stabilizing algorithm guarantees that it always behaves according to its specification. In other words, a snap-stabilizing algorithm is also a self-stabilizing algorithm which stabilizes in 0 steps.
In this paper, we provide the first snap-stabilizing protocol for trie construction. We design particular tries called Proper Greatest Common Prefix (PGCP) Tree. The proposed algorithm arranges the n label values stored in the tree, in average, in O(h + h′) rounds, where h and h′ are the initial and final heights of the tree, respectively. In the worst case, the algorithm requires an O(n) extra space on each node, O(n) rounds and O(n 2) actions. However, simulations show that, using relevant data sets, this worst case is far from being reached and confirm the average complexities, making this algorithm efficient in practice.
This work was developed with financial support from the ANR (Agence Nationale de la Recherche) through the LEGO project referenced ANR-05-CIGC-11.
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Caron, E., Desprez, F., Petit, F., Tedeschi, C. (2007). Snap-Stabilizing Prefix Tree for Peer-to-Peer Systems. In: Masuzawa, T., Tixeuil, S. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2007. Lecture Notes in Computer Science, vol 4838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76627-8_9
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