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Issue No.02 - March/April (2011 vol.8)
pp: 246-255
Chia-Wei Lee , National Cheng Kung University, Tainan
ABSTRACT
Diagnosability is an important metric for measuring the reliability of multiprocessor systems. In this paper, we study the diagnosability of a class of networks, called Two-Matching Composition Networks (2-MCNs), each of which is constructed by connecting two graphs via two perfect matchings. By applying our result to multiprocessor systems, we also compute the diagnosability of folded hypercubes and augmented cubes, both of which belong to two-matching composition networks.
INDEX TERMS
Comparison diagnosis model, diagnosability, graph theory, two-matching composition networks, MM{}^{\ast} model, multiprocessor systems.
CITATION
Chia-Wei Lee, "Diagnosability of Two-Matching Composition Networks under the MM{}^{\ast} Model", IEEE Transactions on Dependable and Secure Computing, vol.8, no. 2, pp. 246-255, March/April 2011, doi:10.1109/TDSC.2009.52
REFERENCES
[1] L.C.P. Albini, S. Chessa, and P. Maestrini, "Diagnosis of Symmetric Graphs under the BGM Model," The Computer J., vol. 47, no. 1, pp. 85-92, 2004.
[2] T. Araki and Y. Shibata, "($t,k$ )-Diagnosable System: A Generalization of the PMC Models," IEEE Trans. Computers, vol. 52, no. 7, pp. 971-975, July 2003.
[3] J.R. Armstrong and F.G. Gray, "Fault Diagnosis in a Boolean $n$ Cube Array of Multiprocessors," IEEE Trans. Computers, vol. 30, no. 8, pp. 587-590, Aug. 1981.
[4] F. Barsi, F. Grandoni, and P. Maestrini, "A Theory of Diagnosability of Digital Systems," IEEE Trans. Computers, vol. 25, no. 6, pp. 585-593, June 1976.
[5] M. Chan, "The Distinguishing Number of the Augmented Cube and Hypercube Powers," Discrete Math., vol. 308, no. 11, pp. 2330-2336, 2008.
[6] G.Y. Chang, G.J. Chang, and G.H. Chen, "Diagnosabilities of Regular Networks," IEEE Trans. Parallel and Distributed Systems, vol. 16, no. 4, pp. 314-323, Apr. 2005.
[7] G.Y. Chang, G.H. Chen, and G.J. Chang, "($t,k$ )-Diagnosis for Matching Composition Networks," IEEE Trans. Computers, vol. 55, no. 1, pp. 88-92, Jan. 2006.
[8] G.Y. Chang, G.H. Chen, and G.J. Chang, "($t,k$ )-Diagnosis for Matching Composition Networks under the MM${}^{\ast}$ Model," IEEE Trans. Computers, vol. 56, no. 1, pp. 73-79, Jan. 2007.
[9] S.A. Choudum and V. Sunitha, "Augmented Cubes," Networks, vol. 40, no. 2, pp. 71-84, 2002.
[10] K.Y. Chwa and L. Hakimi, "On Fault Identification in Diagnosable Systems," IEEE Trans. Computers, vol. 30, no. 6, pp. 414-422, June 1981.
[11] A. Das, K. Thulasiraman, and V.K. Agarwal, "Diagnosis of $t/(t+1)$ -Diagnosable Systems," SIAM J. Computing, vol. 23, no. 5, pp. 895-905, 1994.
[12] P. Dundar, "Augmented Cubes and Its Connectivity Numbers," Neural Network World, vol. 15, no. 1, pp. 1-8, 2005.
[13] A. EI-Awawy and S. Latifi, "Properties and Performance of Folded Hypercubes," IEEE Trans. Parallel and Distributed Systems, vol. 2, no. 1, pp. 31-42, Jan. 1991.
[14] J. Fan, "Diagnosability of the Möbius Cubes," IEEE Trans. Parallel and Distributed Systems, vol. 9, no. 9, pp. 923-928, Sept. 1998.
[15] J. Fan, "Diagnosability of Crossed Cubes under the Comparison Diagnosis Model," IEEE Trans. Parallel and Distributed Systems, vol. 13, no. 7, pp. 687-692, July 2002.
[16] J.F. Fang, "The Bipanconnectivity and $m$ -Panconnectivity of the Folded Hypercube," Theoretical Computer Science, vol. 385, pp. 286-300, 2007.
[17] S.Y. Hsieh and C.N. Kuo, "Hamiltonian-Connectivity and Strongly Hamiltonian-Laceability of Folded Hypercube," Computers and Math. with Applications, vol. 53, pp. 1040-1044, 2007.
[18] S.Y. Hsieh and J.Y. Shiu, "Cycle Embedding of Augmented Cubes," Applied Math. and Computation, vol. 191, no. 2, pp. 314-319, 2007.
[19] A. Kavianpour and K.H. Kim, "Diagnosability of Hypercubes under the Pessimistic One-Step Diagnosis Strategy," IEEE Trans. Computers, vol. 40, no. 2, pp. 232-237, Feb. 1991.
[20] C.N. Lai and G.H. Chen, "Strong Rabin Numbers of Folded Hypercubes," Theoretical Computer Science, vol. 341, nos. 1-3, pp. 196-215, 2005.
[21] C.N. Lai and G.H. Chen, "$\omega$ -Rabin Numbers and Strong $\omega$ -Rabin Numbers of Folded Hypercubes," Networks, vol. 51, no. 3, pp. 171-177, 2008.
[22] J.K. Lee and J.T. Butler, "A Characterization of $t/s$ -Diagnosability and Sequential $t$ -Diagnosability in Designs," IEEE Trans. Computers, vol. 39, no. 10, pp. 1298-1304, Oct. 1990.
[23] M.J. Ma, J.M. Xu, and Z.Z. Du, "Edge-Fault-Tolerant Hamiltonicity of Folded Hypercubes," J. Univ. of Science and Technology of China, vol. 36, no. 3, pp. 244-248, 2006.
[24] M.J. Ma, G.Z. Liu, and J.M. Xu, "Panconnectivity and Edge-Fault-Tolerant Pancyclicity of Augmented Cubes," Parallel Computing, vol. 33, no. 1, pp. 36-42, 2007.
[25] M.J. Ma, G.Z. Liu, and J.M. Xu, "The Super Connectivity of Augmented Cubes," Information Processing Letters, vol. 106, no. 2, pp. 59-63, 2008.
[26] 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.
[27] F.P. Preparata, G. Metze, and R.T. Chien, "On the Connection Assignment Problem of Diagnosable Systems," IEEE Trans. Computers, vol. EC-16, no. 6, pp. 448-454, Dec. 1967.
[28] Y. Saad and M.H. Schultz, "Topological Properties of Hypercubes," IEEE Trans. Computers, vol. 37, no. 7, pp. 867-872, July 1988.
[29] A. Sengupta and A. Dahbura, "On Self-Diagnosable Multiprocessor System: Diagnosis by the Comparison Approach," IEEE Trans. Computers, vol. 41, no. 11, pp. 1386-1396, Nov. 1992.
[30] A.K. Somani, "Sequential Fault Occurrence and Reconfiguration in System Level Diagnosis," IEEE Trans. Computers, vol. 39, no. 12, pp. 1472-1475, Dec. 1990.
[31] A.K. Somani, V.K. Agarwal, and D. Avis, "A Generalized Theory for System Level Diagnosis," IEEE Trans. Computers, vol. 36, no. 5, pp. 538-546, May 1987.
[32] A.K. Somani and O. Peleg, "On Diagnosability of Large Fault Sets in Regular Topology-Based Computer Systems," IEEE Trans. Computers, vol. 45, no. 8, pp. 892-903, Aug. 1996.
[33] D. Wang, "Diagnosability of Hypercubes and Enhanced Hypercubes under the Comparison Diagnosis Model," IEEE Trans. Computers, vol. 48, no. 12, pp. 1369-1374, Dec. 1999.
[34] W.W. Wang, M.J. Ma, and J.M. Xu, "Fault-Tolerant Pancyclicity of Augmented Cubes," Information Processing Letters, vol. 103, no. 2, pp. 52-56, 2007.
[35] J.M. Xu and M.J. Ma, "Cycles in Folded Hypercubes," Applied Math. Letters, vol. 19, no. 2, pp. 140-145, 2006.
[36] J.M. Xu, M.J. Ma, and Z.Z. Du, "Edge-Fault-Tolerant Properties of Hypercubes and Folded Hypercubes," Australasian J. Combinatorics, vol. 35, pp. 7-16, 2006.
[37] M. Xu and J.M. Xu, "The Forwarding Indices of Augmented Cubes," Information Processing Letters, vol. 101, no. 5, pp. 185-189, 2007.
[38] C.L. Yang, G.M. Masson, and R.A. Leonetti, "On Fault Isolation and Identification in $t_{1}/t_{1}$ -Diagnosable Systems," IEEE Trans. Computers, vol. 35, no. 7, pp. 639-643, July 1986.
[39] Q. Zhu and J.M. Xu, "On Restricted Edge Connectivity and Extra Edge Connectivity of Hypercubes and Folded Hypercubes," J. Univ. of Science and Technology of China, vol. 36, no. 3, pp. 249-253, 2006.
[40] Q. Zhu, J.M. Xu, X.M. Hou, and M. Xu, "On Reliability of the Folded Hypercubes," Information Sciences, vol. 177, no. 8, pp. 1782-1788, 2007.
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