The Community for Technology Leaders
RSS Icon
Issue No.02 - February (2009 vol.58)
pp: 251-259
Chieh-Feng Chiang , National Chiao Tung University, Hsinchu
Jimmy J.M. Tan , National Chiao Tung University, Hsinchu
Diagnosis is an essential subject for the reliability of a multiprocessor system. Under the comparison diagnosis model, Sengupta and Dahbura proposed a polynomial-time algorithm with time complexity O(N^{5}) to identify all the faulty processors for a given syndrome in a system with N processors. In this paper, we present a novel idea on system diagnosis called node diagnosability. The node diagnosability can be viewed as a local strategy toward system diagnosability. There is a strong relationship between the node diagnosability and the traditional diagnosability. For this local sense, we focus more on a single processor and require only identifying the status of this particular processor correctly. Under the comparison diagnosis model, we propose a sufficient condition to determine the node diagnosability of a given processor. Furthermore, we propose a useful local structure called an extended star to guarantee the node diagnosability and provide an efficient algorithm to determine the faulty or fault-free status of each processor based on this structure. For a multiprocessor system with total number of processors N, the time complexity of our algorithm to diagnose a given processor is O(\log N) and that to diagnose all the faulty processors is O(N\log N) under the comparison model, provided that there is an extended star structure at each processor and that the time for looking up the testing result of a comparator in the syndrome table is constant.
Fault diagnosis, comparison diagnosis model, MM* diagnosis model, node diagnosability, extended star structure, diagnosis algorithm.
Chieh-Feng Chiang, Jimmy J.M. Tan, "Using Node Diagnosability to Determine t-Diagnosability under the Comparison Diagnosis Model", IEEE Transactions on Computers, vol.58, no. 2, pp. 251-259, February 2009, doi:10.1109/TC.2008.158
[1] S.B. Akers and B. Krishnamurthy, “A Group-Theoretic Model for Symmetric Interconnection Networks,” IEEE Trans. Computers, vol. 38, no. 4, pp. 555-566, Apr. 1989.
[2] T.A. Bartic, J.Y. Mignolet, V. Nollet, T. Marescaux, D. Verkest, S. Vernalde, and R. Lauwereins, “Topology Adaptive Network-on-Chip Design and Implementation,” IEE Proc. Computers and Digital Techniques, vol. 152, no. 4, July 2005.
[3] P. Cull and S. Larson, “The Möbius Cubes,” IEEE Trans. Computers, vol. 44, no. 5, pp. 647-659, May 1995.
[4] A. Dahbura and G. Masson, “An $O(N^{2.5})$ Fault Identification Algorithm for Diagnosable Systems,” IEEE Trans. Computers, vol. 33, no. 6, pp. 486-492, June 1984.
[5] D. König, “Graphen und Matrizen,” Math. Lapok. 38, pp. 116-119, 1931.
[6] E. Egerváry, “On Combinatorial Properties of Matrices (Hungarian with German Summary),” Math. Lapok. 38, pp. 16-28, 1931.
[7] K. Efe, “A Variation on the Hypercube with Lower Diameter,” IEEE Trans. Computers, vol. 40, no. 11, pp. 1312-1316, Nov. 1991.
[8] 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.
[9] J. Fan, “Diagnosability of the Möbius Cubes,” IEEE Trans. Parallel and Distributed Systems, vol. 9, no. 9, pp. 923-928, Sept. 1998.
[10] P. Hilbers, M. Koopman, and J. Snepscheut, “The Twisted Cube,” Proc. Int'l Conf. Parallel Architecture and Languages Europe (PARLE '87), pp. 152-159, June 1987.
[11] P.L. Lai, J.J.M. Tan, C.H. Tsai, and L.H. Hsu, “The Diagnosability of the Matching Composition Network under the Comparison Diagnosis Model,” IEEE Trans. Computers, vol. 53, no. 8, Aug. 2004.
[12] J. Maeng and M. Malek, “A Comparison Connection Assignment for Self-Diagnosis of Multiprocessors Systems,” Proc. 11th Int'l Symp. Fault-Tolerant Computing (FTCS '81), pp. 173-175, 1981.
[13] M. Malek, “A Comparison Connection Assignment for Diagnosis of Multiprocessors Systems,” Proc. Seventh Int'l Symp. Computer Architecture (ISCA '80), pp. 31-36, 1980.
[14] P.P. Pande, C. Grecu, M. Jones, A. Ivonov, and R. Saleh, “Performance Evaluation and Design Trade-Offs for Network-on-Chip Interconnect Architectures,” IEEE Trans. Computers, vol. 54, no. 8, Aug. 2005.
[15] 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.
[16] 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.
[17] 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.
[18] D. Wang, “Diagnosability of Enhanced Hypercubes,” IEEE Trans. Computers, vol. 43, no. 9, pp. 1054-1061, Sept. 1994.
[19] X. Yang and Y.Y. Tang, “Efficient Fault Identification of Diagnosable Systems under the Comparison Model,” IEEE Trans. Computers, vol. 56, no. 12, Dec. 2007.
[20] J. Zheng, S. Latifi, E. Regentova, K. Luo, and X. Wu, “Diagnosability of Star Graphs under the Comparison Diagnosis Model,” Information Processing Letters, vol. 93, pp. 29-36, 2005.
5 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool