Re-rooting algorithm repairs 80,000-node networks with 99.998% recovery

Dense Gaussian networks are algebraic structures with compact diameter and coordinate-based routing, widely used in broadcast systems. However, their broadcast trees are fragile under node, link, or runtime-discovered faults. In a new preprint on arXiv, researcher Bader Albader proposes a re-rooting-assisted runtime repair framework that efficiently heals these networks. The method works by selecting a new root such that known failed nodes become boundary leaves of the broadcast tree whenever possible, then filters failed links and reconnects healthy components using minimal edges—exactly c-1 edges for a connected healthy graph.

The framework also includes deterministic single-link repair, a constant-size boundary-intersection primitive for source selection, and a link-avoidance exclusion test. Large-scale experiments over k ∈ {10, 25, 50, 100, 200} (networks up to 80,401 nodes) with 280,000 static and 15,000 transient trials demonstrate 100% recovery for deterministic and bounded regimes, 99.998% for multi-link faults, and 99.963% for heuristic regimes. Re-rooting reduces average repair edges by 80–100% versus fixed-source repair. Patched Gaussian-link Noxim replays confirm packet-complete execution and show reduced repair edges, components, and depth.

The paper also clarifies that while repair is edge-minimum, completion-cycle latency depends on relocation, scheduling, delivery tail, and selector objective—so universal completion-cycle dominance is not claimed. Overall, this work provides a rigorous, practical solution for maintaining robust broadcast in dense Gaussian networks under realistic failure conditions.