14 papers
Local Fault Repair of Perfect Resource Placements in Eisenstein--Jacobi Networks
Bader Albader
Perfect resource placements in dense Eisenstein--Jacobi (EJ) networks partition the network into hexagonal radius- service cells. This paper studies local repair of such placeme…
Ratio-Independent Three-Cycle Decomposition with Optimal Ordered Local-Switch Cost in Six-Regular Non-Axis Eisenstein--Jacobi Networks
Bader Albader
Six-regular simple Eisenstein--Jacobi (EJ) networks are degree-six quotient-lattice interconnection networks. This paper gives a ratio-independent decomposition of every six-regula…
Re-Rooting-Assisted Edge-Minimum Runtime Repair for Node and Link Failures in Dense Gaussian Broadcast Networks
Bader Albader
Dense Gaussian networks are degree-four algebraic networks with compact diameter and coordinate-based routing. Their diameter-level broadcast trees are efficient but fragile under…
Re-Rooting-Assisted Edge-Minimum Runtime Repair for Node and Link Failures in Dense Eisenstein--Jacobi Broadcast Networks
Bader Albader
One-to-all broadcasting in dense Eisenstein--Jacobi (EJ) networks relies on diameter-level spanning trees that fragment when nodes or links fail. This paper introduces the selected…
Constant-Time Certificate Selection for Local Broadcast Repair in Dense Gaussian and Eisenstein--Jacobi Networks
Bader Albader
Dense Gaussian and Eisenstein--Jacobi (EJ) networks are algebraic interconnection networks with compact coordinate balls, fixed degree, and simple modular addressing. A source-cent…
Multi-Orientation Edge-Minimum Repair for Non-Redundant Fault-Tolerant Broadcasting in Dense Eisenstein--Jacobi Networks
Bader Albader
Dense Eisenstein--Jacobi (EJ) networks are degree-six algebraic interconnection networks whose finite quotient geometry is naturally represented by a hexagonal axial-coordinate bal…
Fault-Tolerant Shared-Relay Communication in Circulant Interconnection Networks
Bader Albader, Galal Hassan, Mohamed R. Al-Mulla
Circulant interconnection networks provide symmetric addressing, compact generator descriptions, and uniform local connectivity. This paper maps a degree--redundancy landscape for…
Closed-Form and Constant-Time New-Source Selection for Fault-Tolerant Broadcasting in Dense Gaussian Networks
Bader Albader
Fault-tolerant broadcasting in dense Gaussian networks is recovered by re-rooting the broadcast at a new source at maximum graph distance from the faulty nodes. This paper extends…
Closed-Form and Constant-Time New-Source Selection for Fault-Tolerant Broadcasting in Dense Eisenstein--Jacobi Networks
Bader Albader
Fault-tolerant broadcasting in dense Eisenstein--Jacobi networks requires efficient recovery when faulty nodes disrupt the original broadcast structure. A re-rooting-based method g…
Re-Rooting-Based Fault-Tolerant One-to-All Broadcasting in Dense Eisenstein--Jacobi Networks
Bader Albader
Dense Eisenstein--Jacobi networks are degree-six algebraic interconnection topologies with regular structure, vertex symmetry, small diameter, and efficient communication algorithm…
Multi-Orientation Edge-Minimum Repair for Non-Redundant Fault-Tolerant Broadcasting in Dense Gaussian Networks
Bader Albader
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 r…
Local Fault Repair of Perfect Resource Placements in Dense Gaussian Networks
Bader Albader
Perfect resource placement in dense Gaussian networks partitions the network into Lee balls centered at resource nodes. The fault-free placement problem is already classified; this…
Re-Rooting-Based Fault-Tolerant Broadcasting in Dense Gaussian Networks
Bader Albader, Mohamed R. Al-Mulla, Galal Hassan
Dense Gaussian networks provide degree-4 interconnection topologies with small diameter and regular structure, making them suitable for efficient one-to-all broadcasting. However,…
A Unified Constant-Time Switch Rule for Constructing Edge-Disjoint Hamiltonian Cycles in Gaussian Networks
Bader Albader
Gaussian networks are degree-four symmetric interconnection networks defined over residue classes of Gaussian integers. Earlier work showed that when the generator satisfi…