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Galal Hassan

Publications and source records attributed to Galal Hassan.

2 recordsLinked to original sources
arXiv2026

Fault-Tolerant Shared-Relay Communication in Circulant Interconnection Networks

Circulant interconnection networks provide symmetric addressing, compact generator descriptions, and uniform local connectivity. This paper maps a degree--redundancy landscape for a fault-tolerant two-hop primitive in directed circulants: given $n$ nodes and degree budget $m$, how large can the worst-case shared-relay multiplicity $R(n,m)$ be? A node is a shared relay for an ordered terminal pair if it has outgoing links to both terminals; an $f$-relay-fault-tolerant circulant requires at least $f+1$ such relays for every pair. The underlying feasibility condition is a cyclic difference-multiplicity condition, which we use as a mathematical tool rather than claim as a new object. The contribution is the network-design framework around this tool: the parameters $R(n,m)$ and $D_f(n)$, a negative theorem for interval circulants, relay-table preprocessing and lookup algorithms, adversarial and random failure guarantees, load-balance scope, certified upper-bound interpretation of heuristic designs, exact small-$n$ calibration, a software lookup-versus-search microbenchmark, and a reproducible study of 526,539 generator sets. The results show that generator choice critically determines worst-case relay survivability: optimized threshold designs achieve $f$-relay-fault tolerance within about $1.16$--$1.63$ of the counting lower bound, while standard interval generators can fail structurally even at much larger degrees.

cs.DC↗
arXiv2026

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

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.

cs.DC↗