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Fault-tolerant cycle embedding in hierarchical cubic networks

✍ Scribed by Jung-Sheng Fu; Gen-Huey Chen

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
184 KB
Volume
43
Category
Article
ISSN
0028-3045

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✦ Synopsis

Abstract

A hierarchical cubic network was proposed as an alternative to the hypercube. By HCN(n), we denote the hierarchical cubic network that contains 2^n^
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 2^2__n__^ − 1 in an HCN(n) with a one‐node fault and fault‐free cycles of length at least 2^2__n__^ − 2__f__ in an HCN(n) with f‐node faults, where 2^2__n__^ is the number of nodes in the HCN(n), f ≤ n − 1 if n = 3 or 4 and f ≤ n if n ≥ 5. Our results can be applied to the hierarchical folded‐hypercube network as well. © 2003 Wiley Periodicals, Inc.

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