Abstract
Stretch is a metric in the construction of spanning trees that measures the deviation in the distance between a pair of nodes in the tree compared to its shortest distance in the underlying graph. This paper proposes a silent self-stabilizing low stretch spanning tree construction protocol BuildTree , that is based on a Low Diameter Decomposition (LDD) technique. The LDD involves steps wherein the graph is decomposed into a small number of connected blocks or clusters, each having a low diameter value. The proposed BuildTree algorithm generates a spanning tree with an average stretch of \(n^{\mathcal {O}(1)}\) and converges to a correct configuration in \(\mathcal {O}(n+\varDelta \cdot \eta )\) rounds, where n, \(\varDelta \) and \(\eta \) is the number of nodes in the graph, the maximum size of a cluster and the number of clusters, respectively. To the best of our knowledge, this is the first known work of using self-stabilization in order to make low stretch tree constructions fault-tolerant.
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Notes
- 1.
It is clear that BuildTree protocol takes \(\mathcal {O}(n\cdot \log n)\) bits of space at each node for its execution.
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Sengupta, S., Peri, S., Anjana, P.S. (2022). A Self-stabilizing Minimum Average Stretch Spanning Tree Construction. In: Koulali, MA., Mezini, M. (eds) Networked Systems. NETYS 2022. Lecture Notes in Computer Science, vol 13464. Springer, Cham. https://doi.org/10.1007/978-3-031-17436-0_9
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