[Paper] Distributed and Autonomic Minimum Spanning Trees

Source: arXiv - 2512.02683v1

Overview

The paper introduces an autonomic algorithm that lets a set of n distributed processes automatically build and keep a minimum‑depth spanning tree. By guaranteeing that each node’s in‑degree and the overall tree depth stay bounded by log₂ n, the approach makes one‑to‑all broadcasts far more scalable than the naïve “every process sends to everyone else” method. The authors also show how the same structure can be used for both best‑effort and reliable broadcast, even when nodes crash and later recover.

Key Contributions

• Logarithmic‑degree spanning tree: Guarantees every node’s degree ≤ log₂ n and tree depth ≤ log₂ n.
• Autonomic construction & repair: The tree is created from any source and self‑heals when up to n – 1 processes fail or re‑join, without centralized coordination.
• VCube‑based virtual topology: Re‑uses the VCube overlay as both the underlying communication fabric and a failure detector.
• Two broadcast primitives: Implements a best‑effort broadcast and a reliable broadcast on top of the autonomic tree.
• Extensive simulation study: Provides performance numbers (latency, message overhead) and compares against classic flooding and static tree approaches.

Methodology

1. Virtual Hypercube (VCube) overlay – Each process is assigned a binary identifier; logical links exist between nodes whose IDs differ in exactly one bit. This yields a hypercube‑like structure where each node has log₂ n neighbors.
2. Tree construction – Starting from a designated root, a node forwards a join message to its VCube neighbors that are currently unconnected. The neighbor that first receives the message becomes the child, and the process repeats recursively. Because the VCube degree is already log₂ n, the resulting spanning tree inherits this bound.
3. Failure detection & repair – Nodes periodically exchange heartbeat messages over their VCube links. If a neighbor stops responding, the node removes the failed child and initiates a re‑join procedure that reconnects the orphaned subtree through alternative VCube links, preserving the logarithmic degree bound.
4. Broadcast algorithms –
   • Best‑effort: The root injects a message that is forwarded down the tree; no acknowledgments are required.
   • Reliable: Each node acknowledges receipt to its parent; missing acks triggers a retransmission along an alternative VCube path, guaranteeing delivery despite crashes.
5. Simulation framework – The authors built a discrete‑event simulator to evaluate latency (tree depth), total messages sent, and resilience under churn (random crash/recovery patterns). They benchmarked against pure flooding and static minimum‑spanning‑tree baselines.

Results & Findings

• Degree bound holds even under massive churn: even when 90 % of nodes crash, the surviving nodes still form a connected tree with degree ≤ log₂ n.
• Latency stays logarithmic: broadcast latency grows only with the tree depth, not with the total number of processes.
• Reliability vs. overhead trade‑off: The reliable version adds a modest number of extra control messages (acknowledgments and retransmissions) but still outperforms flooding by orders of magnitude.

Practical Implications

• Scalable group communication – Distributed services (e.g., microservice meshes, IoT device fleets) can replace expensive all‑to‑all gossip with a lightweight tree that automatically adapts to node failures.
• Fault‑tolerant coordination – Consensus protocols, configuration dissemination, or software‑update rollouts can benefit from the guaranteed connectivity and bounded latency, even in highly dynamic environments.
• Edge & serverless platforms – The VCube overlay requires only local neighbor knowledge, making it suitable for edge nodes that cannot maintain large routing tables.
• Reduced network cost – By limiting each node to O(log n) outgoing messages, bandwidth consumption and CPU overhead drop dramatically compared with naive broadcast, which is crucial for bandwidth‑constrained or battery‑powered devices.
• Plug‑and‑play deployment – Because the tree can be rooted at any process, services can start broadcasting as soon as the first node appears, without a separate bootstrap coordinator.

Limitations & Future Work

• Assumes reliable point‑to‑point links for heartbeat exchange; packet loss could be mistaken for failures, leading to unnecessary reconstructions.
• Simulation‑only validation – Real‑world network heterogeneity (variable latency, asymmetric bandwidth) was not explored; a prototype on a cloud or testbed would strengthen claims.
• Security considerations – The algorithm does not address malicious nodes that could inject false failure reports or disrupt the tree.
• Future directions suggested by the authors include: extending the approach to weighted graphs (optimizing for latency or bandwidth), integrating cryptographic authentication for failure detection, and evaluating the method in large‑scale production systems (e.g., Kubernetes clusters or peer‑to‑peer content distribution networks).

Authors

• Luiz A. Rodrigues
• Elias P. Duarte
• Luciana Arantes

Paper Information

• arXiv ID: 2512.02683v1
• Categories: cs.DC
• Published: December 2, 2025
• PDF: Download PDF