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Fault Tolerance Measures for m-Ary n-Dimensional Hypercubes Based on Forbidden Faulty Sets
August 1998 (vol. 47 no. 8)
pp. 888-893

Abstract—In this paper, we study fault tolerance measures for m-ary n-dimensional hypercubes based on the concept of forbidden faulty sets. In a forbidden faulty set, certain nodes cannot be faulty at the same time and this model can better reflect fault patterns in a real system than the existing ones. Specifically, we study the bounds of the minimum vertex cut set for m-ary n-dimensional hypercubes by requiring each node to have at least k healthy neighbors. Our result enhances and generalizes a result by Latifi et al. for binary hypercubes. Our study also shows that the corresponding result based on the traditional fault model (where k is zero) tends to underestimate network resilience of large networks such as m-ary n-dimensional hypercubes.

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Index Terms:
Fault tolerance, forbidden faulty sets, hypercubes, minimum vertex cut.
Jie Wu, Guanghui Guo, "Fault Tolerance Measures for m-Ary n-Dimensional Hypercubes Based on Forbidden Faulty Sets," IEEE Transactions on Computers, vol. 47, no. 8, pp. 888-893, Aug. 1998, doi:10.1109/12.707589
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