Processor allocation in an N-cube multiprocessor using gray codes
IEEE Transactions on Computers
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
IEEE Transactions on Parallel and Distributed Systems
Embedding a ring in a hypercube with both faulty links and faulty nodes
Information Processing Letters
Topological properties of hierarchical cubic networks
Journal of Systems Architecture: the EUROMICRO Journal
Parallel computation: models and methods
Parallel computation: models and methods
Comments on "Hierarchical Cubic Networks"
IEEE Transactions on Parallel and Distributed Systems
Fault-Free Hamiltonian Cycles in Faulty Arrangement Graphs
IEEE Transactions on Parallel and Distributed Systems
Embed Longest Rings onto Star Graphs with Vertex Faults
ICPP '98 Proceedings of the 1998 International Conference on Parallel Processing
Combinatorial Properties of Hierarchical Cubic Networks
ICPADS '01 Proceedings of the Eighth International Conference on Parallel and Distributed Systems
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A hierarchical cubic network was proposed as an alternative to the hypercube. We use HCN(n) to denote the hierarchical cubic network that contains 2n n-dimensional hypercubes. In this paper, using Gray codes, we construct fault-free hamiltonian cycles in an HCN(n) with n-1 link faults. Since the HCN(n) is regular of degree n+1, the result is optimal. We also construct longest fault-free cycles of length 22n-1 in an HCN(n) with one node fault, and fault-free cycles of length at least 22n-2f in an HCN(n) with f node faults, where 22n is the number of nodes in the HCN(n), f≤n-1 if n=3 or 4, and f≤n if n≥5.