Re-Rooting-Based Fault-Tolerant Broadcasting in Dense Gaussian Networks

Bader Albader; Mohamed R. Al-Mulla; Galal Hassan

doi:10.1109/access.2026.3712557

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arXiv · 2606.16954

Re-Rooting-Based Fault-Tolerant Broadcasting in Dense Gaussian Networks

Bader Albader·Mohamed R. Al-Mulla·Galal Hassan

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Abstract

Dense Gaussian networks provide degree-4 interconnection topologies with small diameter and regular structure, making them suitable for efficient one-to-all broadcasting. However, node failures can disrupt the broadcast process when faulty nodes occupy internal forwarding positions. This paper proposes a lightweight fault-tolerant broadcasting method based on dynamic source relocation, or re-rooting. Instead of constructing redundant spanning trees or backup routing structures, the proposed method selects a new source node so that the faulty nodes are located at graph distance $k$, the network diameter, from the new source. Consequently, faulty nodes become leaf-level nodes in the broadcast process and are not required to forward the message. For the single-fault case, the new source is selected directly from the graph-distance-$k$ boundary of the faulty node. For the two-fault case, we prove that for any pair of faulty nodes in $G(k+(k+1)i)$, there exists a node whose graph distance from both faulty nodes is exactly $k$. The source-selection procedure requires $O(k)$ time. Since the original one-to-all broadcast completes in $k$ parallel steps and the relocation distance is at most $k$, the proposed method completes in at most $2k$ steps in the worst case. We also show that the two-fault guarantee does not generally extend to arbitrary three-fault configurations by giving a counterexample in $G(3+4i)$. Simulation results confirm complete delivery to all non-faulty nodes under the tested one- and two-node failure scenarios, while the baseline broadcast may fail when faulty nodes occur at internal forwarding positions.

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BibTeX RIS

Bader Albader, Mohamed R. Al-Mulla, Galal Hassan. 2026-06-15. Re-Rooting-Based Fault-Tolerant Broadcasting in Dense Gaussian Networks. https://doi.org/10.1109/access.2026.3712557

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