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Diagnosability of Hypercubes and Enhanced Hypercubes under the Comparison Diagnosis Model
December 1999 (vol. 48 no. 12)
pp. 1369-1374

Abstract—In [10], Sengupta and Dahbura discussed how to characterize a diagnosable system under the comparison diagnosis model proposed by Maeng and Malek [7] and a polynomial algorithm was given to identify the faulty processors provided that the system's diagnosability is known. However, for a general system, the determination of its diagnosability is not algorithmically easy. This paper proves that, for the important hypercube-structured multiprocessor systems ($n$-cubes), the diagnosability under the comparison model is $n$ when $n\geq 5$. The paper also studies the diagnosability of enhanced hypercube [11], which is obtained by adding $2^{n-1}$ more links to a regular hypercube of $2^{n}$ processors. It is shown that the augmented communication ability among processors also increases the system's diagnosability under the comparison model. We will prove that the diagnosability is $n+1$ for an enhanced hypercube when $n\geq 6$.

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Index Terms:
Diagnosability, diagnosis by comparison, graph theory, hypercube, interconnection network.
Citation:
Dajin Wang, "Diagnosability of Hypercubes and Enhanced Hypercubes under the Comparison Diagnosis Model," IEEE Transactions on Computers, vol. 48, no. 12, pp. 1369-1374, Dec. 1999, doi:10.1109/12.817401
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