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Issue No.04 - April (2013 vol.62)
pp: 839-843
Sun-Yuan Hsieh , Dept. of Comput. Sci. & Inf. Eng., Nat. Cheng Kung Univ., Tainan, Taiwan
Chi-Ya Kao , Dept. of Comput. Sci. & Inf. Eng., Nat. Cheng Kung Univ., Tainan, Taiwan
ABSTRACT
Processor fault diagnosis plays an important role in measuring the reliability of multiprocessor systems and diagnosing many well-known interconnection networks. Conditional diagnosability is a novel measure of diagnosability that adds the additional condition that any faulty set cannot contain all of the neighbors of any vertex in a system. This study investigates some topological properties of k-ary n-cubes, where k ≥ 4 and n ≥ 4, and shows that the conditional diagnosability of k-ary n-cubes under the comparison diagnosis model is 6n - 5.
INDEX TERMS
multiprocessor interconnection networks, fault diagnosis, topological property, conditional diagnosability, k-ary n-cubes, comparison diagnosis model, processor fault diagnosis, multiprocessor system reliability, interconnection networks, Hypercubes, Computational modeling, Fault diagnosis, Topology, Time measurement, Computer science, interconnection networks, System reliability, comparison diagnosis model, conditional diagnosability, diagnosability, $(k)$-ary $(n)$-cubes
CITATION
Sun-Yuan Hsieh, Chi-Ya Kao, "The Conditional Diagnosability of k-Ary n-Cubes under the Comparison Diagnosis Model", IEEE Transactions on Computers, vol.62, no. 4, pp. 839-843, April 2013, doi:10.1109/TC.2012.18
REFERENCES
 [1] B. Bose, B. Broeg, Y. Kwon, and Y. Ashir, "Lee Distance and Topological Properties of $k$ -Ary $n$ -Cubes," IEEE Trans. Computers, vol. 44, no. 8, pp. 1021-1030, Aug. 1995. [2] N.W. Chang and S.Y. Hsieh, "Conditional Diagnosability of Augmented Cubes under the PMC Model," IEEE Trans. Dependable and Secure Computing, vol. 9, no. 1, pp. 46-60, http://doi.ieeecomputersociety.org/10.1109 TDSC.2010.59, Jan./Feb. 2012. [3] K. Day and A.E. Ai-Ayyoub, "Fault Diameter of $k$ -Ary $n$ -Cube Networks," IEEE Trans. Parallel and Distributed Systems, vol. 8, no. 9, pp. 903-907, Sept. 1997. [4] A.D. Friedman and L. Simoncini, "System-Level Fault Diagnosis," Computer, vol. 13, no. 3, pp. 47-53, 1980. [5] W.S. Hong and S.Y. Hsieh, "Strong Diagnosability and Conditional Diagnosability of Augmented Cubes under the Comparison Diagnosis Model," IEEE Trans. Reliability, vol. 61, no. 1, pp. 140-148, Mar. 2012. [6] G.H. Hsu, C.F. Chiang, L.M. Shih, L.H. Hsu, and J.J.M. Tan, "Conditional Diagnosability of Hypercubes under the Comparison Diagnosis Model," J. Systems Architecture, vol. 55, no. 2, pp. 140-146, 2009. [7] G.H. Hsu and J.J.M. Tan, "Conditional Diagnosability of the BC Networks under the Comparison Diagnosis Model," Proc. Int'l Computer Symp., vol. 1, pp. 269-274, 2008. [8] Y. Ishida, N. Adachi, and H. Tokumaru, "Diagnosability and Distinguishability Analysis and Its Applications," IEEE Trans. Reliability, vol. R-36, no. 5, pp. 531-538, 1987. [9] R.E. Kessler and J.L. Schwarzmeier, "Cray T3D: A New Dimension for Cray Research," Proc. IEEE 38th CS Int'l Conf., pp. 176-182, 1993. [10] P.L. Lai, J.J.M. Tan, C.P. Chang, and L.H. Hsu, "Conditional Diagnosability Measures for Large Multiprocessor Systems," IEEE Trans. Computers, vol. 54, no. 2, pp. 165-175, Feb. 2005. [11] C.K. Lin, J.J.M. Tan, L.H. Hsu, E. Cheng, and L. Lipták, "Conditional Diagnosability of Cayley Graphs Generated by Transposition Trees under the Comparison Diagnosis Model," J. Interconnection Networks, vol. 9, nos. 1/2, pp. 83-97, 2008. [12] C.-K. Lin, T.-L. Kung, and J.J.M. Tan, "An Algorithmic Approach to Conditional-Fault Local Diagnosis of Regular Multiprocessor Interconnected Systems under the PMC Model," IEEE Trans. Computers, vol. 62, no. 3, pp. 439-451, Mar. 2013. [13] J. Maeng and M. Malek, "A Comparison Connection Assignment for Self-Diagnosis of Multiprocessors Systems," Proc. 11th Int'l Symp. Fault-Tolerant Computing, pp. 173-175, 1981. [14] M. Malek, "A Comparison Connection Assignment for Diagnosis of Multiprocessor Systems," Proc. Seventh Ann. Int'l Symp. Computer Architecture, pp. 31-36, 1980. [15] W. Najjar and J.L. Gaudiot, "Network Resilience: A Measure of Network Fault Tolerance," IEEE Trans. Computers, vol. 39, no. 2, pp. 174-181, Feb. 1990. [16] F.P. Preparata, G. Metze, and R.T. Chien, "On the Connection Assignment Problem of Diagnosable Systems," IEEE Trans. Electronic Computers, vol. EC-16, no. 6, pp. 848-854, Dec. 1967. [17] A. Sengupta and A.T. Dahbura, "On Self-Diagnosable Multiprocessor Systems: Diagnosis by the Comparison Approach," IEEE Trans. Computers, vol. 41, no. 11, pp. 1386-1396, Nov. 1992. [18] 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. [19] X. Wang and Q. Zhu, "On Conditional Diagnosability of 3-Ary $n$ -Cubes under the Comparison Diagnosis Model," IEEE Trans. Computers, under review. [20] M. Xu, K. Thulasiraman, and X.D. Hu, "Conditional Diagnosability of Matching Composition Networks under the PMC Model," IEEE Trans. Circuits and Systems, vol. 56, no. 11, pp. 875-879, Nov. 2009. [21] M.C. Yang, J.M. Tam, and L.H. Hsu, "Hamiltonian Circuit and Linear Array Embeddings in Faulty $k$ -Ary $n$ -Cubes," J. Parallel and Distributed Computing, vol. 67, pp. 362-368, 2007. [22] Q. Zhu, "On Conditional Diagnosability and Reliability of the BC Networks," The J. Supercomputing, vol. 45, no. 2, pp. 173-184, 2008.