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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 $n\geq 6$.

[1] J.R. Armstrong and F.G. Gray, “Fault Diagnosis in a Boolean$n$Cube Array of Microprocessors,” IEEE Trans. Computers, vol. 30, no. 8, pp. 587-590, Aug. 1981.
[2] W.D. Hillis, The Connection Machine, MIT Press, Cambridge, Mass., 1985.
[3] J.P. Hayes, T.N. Mudge, and Q.F. Stout, “Architecture of a Hypercube Supercomputer,” Proc. 1986 Int'l Conf. Parallel Processing, pp. 653-660, Aug. 1986.
[4] Intel Corporation, iPSC System Overview, Jan. 1986.
[5] A. Kavianpour and K.H. Kim, “Diagnosability of Hypercube under the Pessimistic One-Step Diagnosis Strategy,” IEEE Trans. Computers, vol. 40, no. 2, pp. 232-237, Feb. 1991.
[6] M. Malek, “A Comparison Connection Assignment for Diagnosis of Multiprocessor Systems,” Proc. Seventh Int'l Symp. Computer Architecture, pp. 31-35, 1980.
[7] J. Maeng and M. Malek, “A Comparison Connection Assignment for Self-Diagnosis of Multiprocessor Systems,” Proc. 11th Int'l Symp. Fault-Tolerant Computing, pp. 173-175, 1981.
[8] F.P. Preparata, G. Metze, and R.T. Chien, “On the Connection Assignment Problem of Diagnosable Systems,” IEEE Trans. Electronic Computers, vol. 16, no. 12, pp. 848-854, Dec. 1967.
[9] C. L. Seitz,“The cosmic cube,”CACM, vol. 28, pp. 22–33, Jan. 1985.
[10] A. Sengupta and A. Dahbura, “On Self-Diagnosable Multiprocessor Systems: Diagnosis by the Comparison Approach,” IEEE Trans. Computers, vol. 41, no. 11, pp. 1386-1396, Nov. 1992.
[11] N.-F. Tzeng and S. Wei, “Enhanced Hypercubes,” IEEE Trans. Computers, vol. 40, no. 3, pp. 284-294, Mar. 1991.
[12] D. Wang, “Diagnosability of Enhanced Hypercubes,” IEEE Trans. Computers, vol. 43, no. 9, pp. 1,054-1,061, Sept. 1994.

Index Terms:
Diagnosability, diagnosis by comparison, graph theory, hypercube, interconnection network.
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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