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Issue No.02 - Feb. (2013 vol.62)
pp: 259-267
Chang-Hsiung Tsai , National Dong Hwa University, Hualien
ABSTRACT
Processor fault diagnosis is an essential subject for the reliability of a multiprocessor system. The precise strategy and the pessimistic strategy are two classical diagnostic strategies which are based on the well-known PMC model. The precise strategy problem of fault diagnosis is discussed widely and demands that all processors be identified correctly, specifically that all fault-free processors are identified as "fault free” and all faulty processors are identified as "faulty.” The pessimistic diagnosis strategy is a process to diagnose faults that allows all faulty processors to be isolated within a set that contains at most one fault-free processor. In this paper, we study the pessimistic diagnosis strategy under the PMC model for hypercube-like multiprocessor systems. The contribution is to propose an efficient pessimistic diagnosis algorithm for hypercube-like multiprocessor systems. If we denote by N the total number of processors in the hypercube-like system to be diagnosed, the algorithm can run in O(N) time.
INDEX TERMS
Program processors, Fault diagnosis, Hypercubes, Multiprocessing systems, Algorithm design and analysis, Complexity theory, Testing, hypercube-like, Reliable system, system-level diagnosis, the PMC model, pessimistic strategy
CITATION
Chang-Hsiung Tsai, "A Quick Pessimistic Diagnosis Algorithm for Hypercube-Like Multiprocessor Systems under the PMC Model", IEEE Transactions on Computers, vol.62, no. 2, pp. 259-267, Feb. 2013, doi:10.1109/TC.2011.228
REFERENCES
[1] S. Akram, A. Papakonstantinou, R. Kumar, and D. Chen, “A Workload-Adaptive and Reconfigurable Bus Architecture for Multicore Processors,” Int'l J. Reconfigurable Computing, vol. 2010, doi:10.1155/2010/205852, 2010.
[2] 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.
[3] 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, Jan./Feb. 2011.
[4] P. Cull and S.M. Larson, “The Möbius Cubes,” IEEE Trans. Computers, vol. 44, no. 5, pp. 647-659, May 1995.
[5] K. Efe, “The Crossed Cube Architecture for Parallel Computing,” IEEE Trans. Parallel and Distributed Systems, vol. 3, no. 5, pp. 513-524, Sept. 1992.
[6] A. El-Amawy and S. Latifi, “Properties and Performance of Folded Hypercubes,” IEEE Trans. Parallel and Distributed Systems, vol. 2, no. 1, pp. 31-42, Jan. 1991.
[7] J. Fan, “Diagnosability of the Möbius Cubes,” IEEE Trans. Parallel and Distributed Systems, vol. 9, no. 9, pp. 923-928, Sept. 1998.
[8] J. Fan and L. He, “BC Interconnection Networks and Their Properties,” Chinese J. Computers, vol. 26, no. 1, pp. 84-90, 2003.
[9] J. Fan and X. Lin, “The $t/k$ -Diagnosability of the BC Graphs,” IEEE Trans. Computers, vol. 54, no. 2, pp. 176-184, Feb. 2005.
[10] M.R.B. Forshaw, K. Nikolic, and A. Sadek, Third Ann. Report, Autonomous Nanoelectronic Systems with Extended Replication and Signalling, ANSWERS, technical report, Univ. College London, Image Processing Group, London, U.K. http://ipga. phys.ucl.ac.uk/research/answers/ reports3rd_year_UCL.pdf, 2011.
[11] P.A.J. Hilbers, M.R.J. Koopman, and J.L.A. van de Snepscheut, “The Twisted Cubes,” Proc. Parallel Architectures on PARLE: Parallel Architectures and Languages Europe, pp. 152-158, 1987.
[12] A. Kavianpour and A.D. Friedman, “Efficient Design of Easily Diagnosable System,” Proc. Third USA-Japan Computer Conf., 1978.
[13] A. Kavianpour and K.H. Kim, “Diagnosabilities of Hypercubes under the Pessimistic One-Step Diagnosis Strategy,” IEEE Trans. Computers, vol. 40, no. 2, pp. 232-237, Feb. 1991.
[14] A. Kavianpour, “Sequential Diagnosability of Star Graphs,” Computers and Electrical Eng., vol. 22, no. 1, pp. 37-44, 1996.
[15] D. Kissler, F. Hannig, A. Kupriyanov, and J. Teich, “A Highly Parameterizable Parallel Processor Array Architecture,” Proc. IEEE Int'l Conf. Field Programmable Technology (FPT), pp. 105-112, Dec. 2006.
[16] 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.
[17] F.T. Leighton, Introduction to Parallel Algorithms and Architecture: Arrays, Trees, Hypercubes. Morgan Kaufmann, 1992.
[18] C.K. Lin, T.L. Kung, J.J.M. Tan, “Conditional-Fault Diagnosability of Multiprocessor Systems with an Efficient Local Diagnosis Algorithm under the PMC Model,” IEEE Trans. Parallel and Distributed Systems, vol. 22, no. 10, pp. 1669-1680, Oct. 2011.
[19] F.P. Preparata, G. Metze, and R.T. Chien, “On the Connection Assignment Problem of Diagnosis Systems,” IEEE Trans. Electronic Computers, vol. 16, no. 12, pp. 848-854, Dec. 1967.
[20] T. Szymanski, “Hypermeshes: Optical Interconnection Networks for Parallel Computing,” J. Parallel and Distributed Computing., vol. 26, pp. 1-23, 1995.
[21] A.S. Vaidya, P.S.N. Rao, and S.R. Shankar, “A Class of Hypercube-Like Networks,” Proc. IEEE Fifth Symp. Parallel and Distributed Processing, pp. 800-805, 1993.
[22] D. Wang, “Diagnosability of Enhanced Hypercubes,” IEEE Trans. Computers, vol. 43, no. 9, pp. 1054-1061, Sept. 1994.
[23] M. Xu, K. Thulasiraman, X.D. Hu, “Conditional Diagnosability of Matching Composition Networks under the PMC Model,” IEEE Trans. Circuits and Systems II: Express Briefs, vol. 56, no. 11, pp. 875-879, Nov. 2009.
[24] 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.
[25] X. Yang, “A Fast Pessimistic One-Step Diagnosis Algorithm for Hypercube Multicomputer Systems,” J. Parallel and Distributed Computing, vol. 64, pp. 546-553, 2004.
[26] X. Yang, S.M. Tang, and J.M. Megson, “The Locally Twisted Cube,” Int'l J. Computer Math., vol. 82, pp. 401-413, 2005.
[27] E. Yang, X. Yang, Q. Dong, J. Li, “Conditional Diagnosability of Hypermesh Optical Multiprocessor Systems under the Pmc Model,” Int'l J. Computer Math., vol. 88, pp. 2275-2284, 2011.
[28] Q. Zhu, S.Y. Liu, M. Xu, “On Conditional Diagnosability of the Folded Hypercubes,” Information Sciences, vol. 178, no. 4, pp. 1069-1077, 2008.
[29] Q. Zhu, “On Conditional Diagnosability and Reliability of the BC Networks,” J. Supercomputing, vol. 45, no. 2, pp. 173-184, 2008.
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