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Issue No.06 - June (2008 vol.57)
pp: 721-732
ABSTRACT
The notion of diagnosability has long played an important role in measuring the reliability of multiprocessor systems. Such a system is $t$-diagnosable if all faulty nodes can be identified without replacement when the number of faults does not exceed $t$, where $t$ is some positive integer. Furthermore, a system is strongly $t$-diagnosable if it can achieve $(t+1)$-diagnosability, except for the case where a node's neighbors are all faulty. In this paper, we investigate the strong diagnosability of a class of product networks, under the comparison diagnosis model. Based on our results, we can determine the strong diagnosability of several widely used multiprocessor systems, such as hypercubes, mesh-connected $k$-ary $n$-cubes, torus-connected $k$-ary $n$-cubes, and hyper Petersen networks.
INDEX TERMS
Reliability, Testing, and Fault-Tolerance, Fault tolerance, Measurement, evaluation, modeling, simulation of multiple-processor systems, On-chip interconnection networks, Graph Theory, Discrete Mathematics, Mathematics of Computing, Network problems, Graph Theory, Discrete Mathematics, Mathematics of Computing
CITATION
Sun-Yuan Hsieh, Yu-Shu Chen, "Strongly Diagnosable Product Networks Under the Comparison Diagnosis Model", IEEE Transactions on Computers, vol.57, no. 6, pp. 721-732, June 2008, doi:10.1109/TC.2008.30
REFERENCES
 [1] T. Araki and Y. Shibata, “Diagnosability of Networks Represented by the Cartesian Product,” IEICE Trans. Fundamentals, vol. E83-A, no. 3, pp. 465-470, 2000. [2] 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. [3] S. Bettayeb, “On the $k\hbox{-}{\rm Ary}$ Hypercube,” Theoretical Computer Science, vol. 140, no. 2, pp. 333-339, 1995. [4] B. Bose, B. Broeg, Y. Kwon, and Y. Ashir, “Lee Distance and Topological Properties of $k\hbox{-}{\rm Ary}$ $n\hbox{-}{\rm Cubes}$ ,” IEEE Trans. Computers, vol. 44, no. 8, pp. 1021-1030, Aug. 1995. [5] L.N. Bhuyan and D.P. Agrawal, “Generalized Hypercube and Hyperbus Structures for a Computer Network,” IEEE Trans. Computers, vol. 33, no. 4, pp. 323-333, Apr. 1984. [6] D.M. Blough, G.F. Sullivan, and G.M. Masson, “Efficient Diagnosis of Multiprocessor System under Probabilistic Models,” IEEE Trans. Computers, vol. 41, no. 9, pp. 1126-1136, Sept. 1992. [7] C.P. Chang, P.L. Lai, J.J.M. Tan, and L.H. Hsu, “Diagnosability of $t\hbox{-}{\rm Connected}$ Networks and Product Networks under the Comparison Diagnosis Model,” IEEE Trans. Computers, vol. 53, no. 12, pp.1582-1590, Dec. 2004. [8] S.K. Das, S.R. Öhring, and A.K. Banerjee, “Embeddings Into Hyper Petersen Network: Yet Another Hypercube-Like Interconnection Topology,” VLSI Design, vol. 2, no. 4, pp. 335-351, 1995. [9] 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. [10] G.Y. Chang, G.H. Chen, and G.J. Chang, “$(t, k)\hbox{-}{\rm Diagnosis}$ for Matching Composition Networks,” IEEE Trans. Computers, vol. 55, no. 1, pp. 88-92, Jan. 2006. [11] G.Y. Chang, G.H. Chen, and G.J. Chang, “$(t, k)\hbox{-}{\rm Diagnosis}$ for Matching Composition Networks under the ${\rm MM}^{\ast}$ Model,” IEEE Trans. Computers, vol. 56, no. 1, pp. 73-79, Jan. 2007. [12] K.Y. Chwa and L. Hakimi, “On Fault Identification in Diagnosable Systems,” IEEE Trans. Computers, vol. 30, no. 6, pp. 414-422, June 1981. [13] W.S. Chiue and B.S. Shieh, “On Connectivity of the Cartesian Product of Two Graphs,” Applied Math. and Computation, vol. 102, nos. 2-3, pp. 129-137, 1999. [14] A. Das, K. Thulasiraman, and V.K. Agarwal, “Diagnosis of $t/(t + 1)\hbox{-}{\rm Diagnosable}$ Systems,” SIAM J. Computing, vol. 23, no. 5, pp.895-905, 1994. [15] K. Day and A.E. Al-Ayyoub, “The Cross Product of Interconnection Networks,” IEEE Trans. Parallel and Distributed Systems, vol. 8, no. 2, pp. 109-118, Feb. 1997. [16] K. Day and A.E. Al-Ayyoub, “Minimal Fault Diameter for Highly Resilient Product Networks,” IEEE Trans. Parallel and Distributed Systems, vol. 11, no. 9, pp. 926-930, Sept. 2000. [17] K. Efe and A. Fernandez, “Products of Networks with Logarithmic Diameters and Fixed Degree,” IEEE Trans. Parallel and Distributed Systems, vol. 6, no. 9, pp. 963-975, Sept. 1995. [18] T. El-Ghazawi and A. Youssef, “A Generalized Framework for Developing Adaptive Fault-Tolerant Routing Algorithms,” IEEE Trans. Reliability, vol. 42, no. 2, pp. 250-258, 1993. [19] J. Fan, “Diagnosability of the Möbius Cubes,” IEEE Trans. Parallel and Distributed Systems, vol. 9, no. 9, pp. 923-928, Sept. 1998. [20] 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. [21] H. Fugiwara and K. Kinoshita, “On the Computational Complexity of System Diagnosis,” IEEE Trans. Computers, vol. 27, no. 10, pp. 881-885, Oct. 1978. [22] S.L. Hakimi and A.T. Amin, “Characterization of Connection Assignment,” IEEE Trans. Computers, vol. 23, pp. 86-88, 1974. [23] 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. [24] S. Khanna and W.K. Fuchs, “A Graph Partitioning Approach to Sequential Diagnosis,” IEEE Trans. Computers, vol. 46, no. 1, pp.39-47, Jan. 1997. [25] S.C. Ku, B.F. Wang, and T.K. Hung, “Constructing Edge-Disjoint Spanning Trees on Product Networks,” IEEE Trans. Parallel and Distributed Systems, vol. 14, no. 3, pp. 213-221, Mar. 2003. [26] S. Ohring and D.H. Hohndel, “Optimal Fault Tolerant Communication Algorithms on Product Networks Using Spanning Trees,” Proc. Sixth IEEE Symp. Parallel and Distributed Processing, pp. 188-195, 1994. [27] J.K. Lee and J.T. Butler, “A Characterization of $t/s\hbox{-}{\rm Diagnosability}$ and Sequential $t\hbox{-}{\rm Diagnosability}$ in Designs,” IEEE Trans. Computers, vol. 39, no. 10, pp. 1298-1304, Oct. 1990. [28] M. Malek, “A Comparison Connection Assignment for Diagnosable of Multiprocessor Systems,” Proc. Seventh Ann. Int'l Symp. Computer Architecture, pp. 31-36, 1980. [29] 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. [30] F.P. Preparata, G. Metze, and R.T. Chien, “On the Connection Assignment Problem of Diagnosable Systems,” IEEE Trans. Computers, vol. 16, pp. 448-454, 1967. [31] A.L. Rosenberg, “Product-Shuffle Networks: Towards Reconciling Shuffles and Butterflies,” Discrete Applied Math., vols. 37/38, pp.465-488, 1992. [32] Y. Saad and M.H. Schultz, “Topological Properties of Hypercubes,” IEEE Trans. Computers, vol. 37, no. 7, pp. 867-872, July 1988. [33] 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. [34] 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. [35] D. Wang, “Diagnosability of Enhanced Hypercubes,” IEEE Trans. Computers, vol. 43, no. 9, pp. 1054-1061, Sept. 1994. [36] 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. [37] C.L. Yang, G.M. Masson, and R.A. Leonetti, “On Fault Isolation and Identification in $t_{1}/t_{1}\hbox{-}{\rm Diagnosable}$ Systems,” IEEE Trans. Computers, vol. 35, no. 7, pp. 639-643, July 1986.
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