A fault tolerant massively parallel processing architecture
Journal of Parallel and Distributed Computing
The Cubical Ring Connected Cycles: A Fault Tolerant Parallel Computation Network
IEEE Transactions on Computers
Design and Analysis of Dynamic Redundancy Networks
IEEE Transactions on Computers
Interconnection networks for large-scale parallel processing: theory and case studies (2nd ed.)
Interconnection networks for large-scale parallel processing: theory and case studies (2nd ed.)
Designing fault-tolerant systems using automorphisms
Journal of Parallel and Distributed Computing
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
CSC '93 Proceedings of the 1993 ACM conference on Computer science
A Versatile Ring-Connected Hypercube
IEEE Micro
The cube-connected cycles: a versatile network for parallel computation
Communications of the ACM
Line Digraph Iterations and Connectivity Analysis of de Bruijn and Kautz Graphs
IEEE Transactions on Computers
Periodically Regular Chordal Rings
IEEE Transactions on Parallel and Distributed Systems
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In this paper, we first reviewed a 1-fault-tolerant (1-ft) hypercube model with degree 2r, the ring-connected network (RCN), which has the lowest degree among all 1-ft, one spare node, r-dimensional hypercube architecture yet discovered. Then we proposed a constant-time reconfiguration algorithm via an add-and-modulo automorphism. Furthermore, by introducing the equivalence from hypercubes to cube-connected cycles (CCCs) and to butterflies (BFs), we find there is also a corresponding equivalence from RCNs to cubical ring connected cycles (CRCCs) and to dynamic redundancy networks (DRNs). From this fact, we find out that once a symmetric fault-tolerant structure has been discovered for one of the three models, then it can apply directly to the other hypercubic networks. Applying the technique, we find a degree 6, 1-ft Benes network. Another point is we think that the strong relationship between hypercubes, CCCs and BFs should be paid more attention, and finally from this equivalence relationship we propose three new bounded-degree k-ft models: k-ft CCCs, k-ft BFs, and k-ft Benes networks.