Publication 2008 Issue No. 12 - December Abstract - Strongly Diagnosable Systems under the Comparison Diagnosis Model
Strongly Diagnosable Systems under the Comparison Diagnosis Model
December 2008 (vol. 57 no. 12)
pp. 1720-1725
 ASCII Text x Sun-Yuan Hsieh, Yu-Shu Chen, "Strongly Diagnosable Systems under the Comparison Diagnosis Model," IEEE Transactions on Computers, vol. 57, no. 12, pp. 1720-1725, December, 2008.
 BibTex x @article{ 10.1109/TC.2008.104,author = {Sun-Yuan Hsieh and Yu-Shu Chen},title = {Strongly Diagnosable Systems under the Comparison Diagnosis Model},journal ={IEEE Transactions on Computers},volume = {57},number = {12},issn = {0018-9340},year = {2008},pages = {1720-1725},doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2008.104},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - Strongly Diagnosable Systems under the Comparison Diagnosis ModelIS - 12SN - 0018-9340SP1720EP1725EPD - 1720-1725A1 - Sun-Yuan Hsieh, A1 - Yu-Shu Chen, PY - 2008KW - DiagnosticsKW - TopologyKW - DiagnosticsKW - Graph TheoryKW - Network problemsVL - 57JA - IEEE Transactions on ComputersER -
Sun-Yuan Hsieh, National Cheng Kung University, Tainan
Yu-Shu Chen, National Cheng Kung University, Tainan
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 is $t$-diagnosable and can achieve $(t+1)$-diagnosable except for the case where a node's neighbors are all faulty. In this paper, we propose some conditions for verifying whether a class of interconnection networks, called Matching Composition Networks (MCNs), are strongly diagnosable under the comparison diagnosis model.

[1] T. Araki and Y. Shibata, “$(t, k)\hbox{-}{\rm Diagnosable}$ System: A Generalization of the PMC Models,” IEEE Trans. Computers, vol. 52, no. 7, pp. 971-975, July 2003.
[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] 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.
[4] 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.
[5] 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.
[6] P. Cull and S.M. Larson, “The Möbius Cubes,” IEEE Trans. Computers, vol. 44, no. 5, pp. 647-659, May 1995.
[7] K.Y. Chwa and L. Hakimi, “On Fault Identification in Diagnosable Systems,” IEEE Trans. Computers, vol. 30, no. 6, pp. 414-422, June 1981.
[8] 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, May 1994.
[9] K. Efe, “A Variation on the Hypercube with Lower Diameter,” IEEE Trans. Computers, vol. 40, no. 11, pp. 1312-1316, Nov. 1991.
[10] J. Fan, “Diagnosability of the Möbius Cubes,” IEEE Trans. Parallel and Distributed Systems, vol. 9, no. 9, pp. 923-928, Sept. 1998.
[11] 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.
[12] J. Fan and X. Lin, “The $t/k\hbox{-}{\rm Diagnosability}$ of the BC Graphs,” IEEE Trans. Computers, vol. 54, no. 2, pp. 176-184, Feb. 2005.
[13] P.A.J. Hilbers, M.R.J. Koopman, and J.L.A. van de Snepscheut, “The Twisted Cube,” Proc. Parallel Architectures and Languages Europe (PARLE '87), pp. 152-159, June 1987.
[14] 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.
[15] 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.
[16] P. Kulasinghe, “Connectivity of the Crossed Cube,” Information Proc. Letters, vol. 61, no. 4, pp. 221-226, Feb. 1997.
[17] P.L. Lai, J.J.M. Tan, C.H. Tsai, and L.H. Hsu, “Diagnosability of the Matching Composition Network under the Comparison Diagnosis Model,” IEEE Trans. Computers, vol. 53, no. 8, pp. 1064-1069, Aug. 2004.
[18] 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.
[19] J. Maeng and M. Malek, “A Comparison Connection Assignment for Self-Diagnosis of Multiprocessor Systems,” Proc. 11th Int'l Symp. Fault-Tolerant Computing (FTCS '81), pp. 173-175, 1981.
[20] 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, Dec. 1967.
[21] Y. Saad and M.H. Schultz, “Topological Properties of Hypercubes,” IEEE Trans. Computers, vol. 37, no. 7, pp. 867-872, July 1988.
[22] 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.
[23] 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.
[24] 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.
[25] 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.
[26] 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.
[27] X. Yang, D.J. Evans, and G.M. Megson, “The Locally Twisted Cubes,” Int'l J. Computer Math., vol. 82, no. 4, pp. 401-413, Apr. 2005.
[28] X. Yang and Y.Y. Tang, “Efficient Fault Identification of Diagnosable Systems under the Comparison Model,” IEEE Trans. Computers, vol. 56, no. 12, pp. 1612-1618, Dec. 2007.

Index Terms:
Diagnostics, Topology, Diagnostics, Graph Theory, Network problems
Citation:
Sun-Yuan Hsieh, Yu-Shu Chen, "Strongly Diagnosable Systems under the Comparison Diagnosis Model," IEEE Transactions on Computers, vol. 57, no. 12, pp. 1720-1725, Dec. 2008, doi:10.1109/TC.2008.104