Multi-Orientation Edge-Minimum Repair for Non-Redundant Fault-Tolerant Broadcasting in Dense Gaussian Networks

Computer Science > Distributed, Parallel, and Cluster Computing [Submitted on 16 Jun 2026] Title:Multi-Orientation Edge-Minimum Repair for Non-Redundant Fault-Tolerant Broadcasting in Dense Gaussian Networks View PDF HTML (experimental)Abstract:Dense Gaussian networks are degree-four algebraic interconnection networks with compact diameter and simple modular routing. This paper studies non-redundant one-to-all broadcast repair in the dense Gaussian network generated by $\alpha=k+(k+1)i$. We propose multi-orientation edge-minimum repair (MOEM), which evaluates a constant-size family of Gaussian broadcast-tree orientations, selects a fault-aware orientation, contracts the fault-pruned tree into healthy components, and reconnects those components using external component-crossing repair edges. The resulting structure is a rooted spanning tree of the healthy subgraph, so each healthy node receives the message exactly once and no faulty node is used. We prove that, for a chosen orientation with $c$ fault-pruned components and a connected healthy component graph, the repair step is non-redundant and uses the minimum possible number $c-1$ of external component-repair edges. We also prove that, for every one- or two-fault placement, the MOEM orientation family contains a repair with depth at most $k+2$. The depth proof combines a certificate framework, an explicit four-case off-axis analysis, and a five-component orthogonal-axis certificate. Exhaustive validation for $k=5,\ldots,10$ and large-scale validation through $k=200$ confirm the implementation and show that random two-fault repairs use approximately two external repair edges. Submission history From: Bader Albader Dr. [view email][v1] Tue, 16 Jun 2026 05:11:05 UTC (2,974 KB) Current browse context: cs.DC References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.