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Fault-tolerant embeddings of Hamiltonian circuits in k-ary n-cubes.

Ashir, Y. A. and Stewart, I. A. (2002) 'Fault-tolerant embeddings of Hamiltonian circuits in k-ary n-cubes.', SIAM journal on discrete mathematics., 15 (3). pp. 317-328.


We consider the fault-tolerant capabilities of networks of processors whose underlying topology is that of the k-ary n-cube $Q_n^k$, where k > 2 and n > 1. In particular, given a copy of $Q_n^k$ where some of the inter-processor links may be faulty but where every processor is incident with at least two healthy links, we show that if the number of faults is at most 4n-5 then $Q_n^k$ still contains a Hamiltonian circuit; but that there are situations where the number of faults is 4n-4 (and every processor is incident with at least two healthy links) and no Hamiltonian circuit exists. We also remark that given a faulty $Q_n^k$, the problem of deciding whether there exists a Hamiltonian circuit is NP-complete.

Item Type:Article
Keywords:Interconnection networks, Fault-tolerance, NP-completeness.
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Publisher statement:© 2002 Society for Industrial and Applied Mathematics.
Date accepted:No date available
Date deposited:08 October 2008
Date of first online publication:January 2002
Date first made open access:No date available

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