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Durham University

Computer Science


Publication details for Professor Iain Stewart

Ashir, Y.A. & Stewart, I.A. (2002). Fault-tolerant embeddings of Hamiltonian circuits in k-ary n-cubes. SIAM Journal On Discrete Mathematics 15(3): 317-328.

Author(s) from Durham


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.