Publication 2006 Issue No. 1 - January Abstract - (t,k)-Diagnosis for Matching Composition Networks
 This Article Share Bibliographic References Add to: Digg Furl Spurl Blink Simpy Google Del.icio.us Y!MyWeb Search Similar Articles Articles by Guey-Yun Chang Articles by Gen-Huey Chen Articles by Gerard J. Chang
(t,k)-Diagnosis for Matching Composition Networks
January 2006 (vol. 55 no. 1)
pp. 88-92
 ASCII Text x Guey-Yun Chang, Gen-Huey Chen, Gerard J. Chang, "(t,k)-Diagnosis for Matching Composition Networks," IEEE Transactions on Computers, vol. 55, no. 1, pp. 88-92, January, 2006.
 BibTex x @article{ 10.1109/TC.2006.1,author = {Guey-Yun Chang and Gen-Huey Chen and Gerard J. Chang},title = {(t,k)-Diagnosis for Matching Composition Networks},journal ={IEEE Transactions on Computers},volume = {55},number = {1},issn = {0018-9340},year = {2006},pages = {88-92},doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2006.1},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - (t,k)-Diagnosis for Matching Composition NetworksIS - 1SN - 0018-9340SP88EP92EPD - 88-92A1 - Guey-Yun Chang, A1 - Gen-Huey Chen, A1 - Gerard J. Chang, PY - 2006KW - Index Terms- DiagnosabilityKW - matching composition networkKW - multiprocessor systemKW - PMC modelKW - precise diagnosis strategyKW - sequential diagnosisKW - (tKW - k){\hbox{-}}{\rm diagnosis}.VL - 55JA - IEEE Transactions on ComputersER -
(t,k){\hbox{-}}{\rm diagnosis}, which is a generalization of sequential diagnosis, requires at least k faulty processors identified and replaced in each iteration provided there are at most t faulty processors, where t \ge k. This paper proposes a (t,k){\hbox{-}}{\rm diagnosis} algorithm for matching composition networks, which include many well-known interconnection networks such as hypercubes, crossed cubes, twisted cubes, and Möbius cubes. It is shown that matching composition networks of n dimensions are (\Omega({\frac{2^n*\log n}{n}}), n){\hbox{-}}{\rm diagnosable}, where n>5.

[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] T. Araki and Y. Shibata, “Diagnosability of Butterfly Networks under the Comparison Approach,” IEICE Trans. Fundamentals of Electronics Comm. and Computer Science, vol. E85-A, no. 5, pp. 1152-1160, 2002.
[3] J.R. Armstrong and F.G. Gray, “Fault Diagnosis in a Boolean $n{\hbox{-}}{\rm Cube}$ Array of Microprocessors,” IEEE Trans. Computers, vol. 30, no. 8, pp. 587-590, Aug. 1981.
[4] G.Y. Chang, G.H. Cheng, and G.J. Chang, “$(t,k) {\hbox{-}}{\rm Diagnosis}$ for Matching Composition Networks under the Comparison Diagnosis Model,” in preparation.
[5] 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, pp. 1582-1590, 2004.
[6] P. Cull and S.M. Larson, “The Möbius Cubes,” IEEE Trans. Computers, vol. 44, no. 5, pp. 647-659, May 1995.
[7] A.T. Dahbura, “System-Level Diagnosis: A Perspective for the Third Decade,” Concurrent Computation: Algorithms, Architectures, Technologies, New York: Plenum, 1988.
[8] A.T. Dahabura and G.M. Masson, “An $O(n^{2. 5})$ Fault Identification Algorithm for Diagnosable Systems,” IEEE Trans. Computers, vol. 33, no. 6, pp. 486-492, June 1984.
[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. 923-927, 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] A.D. Friedman and L. Simoncini, “System-Level Fault Diagnosis,” The Computer J., vol. 13, no. 3, pp. 47-53, 1980.
[13] A.D. Friedman, “A New Measure of Digital System Diagnosis,” Digest Int'l Symp. Fault-Tolerant Computing, pp. 167-170, 1975.
[14] H. Fujiwara and K. Kinoshita, “On the Computational Complexity of System Diagnosis,” IEEE Trans. Computers, vol. 27, no. 10, pp. 881-885, Oct. 1978.
[15] S.L. Hakimi and A.T. Amin, “Characterization of Connection Assignment,” IEEE Trans. Computers, vol. 23, pp. 86-88, 1974.
[16] S. Hart, “A Note on the Edges of the $n{\hbox{-}}{\rm Cube}$ ,” Discrete Math., vol. 14, pp. 157-163, 1976.
[17] P.A.J. Hilbers, M.R.J. Koopman, and J.L. A. van de Snepscheut, “The Twisted Cubes,” Proc. Parallel Architecture and Language Europe, pp. 152-159, June 1987.
[18] A. Kavianpour, “Sequential Diagnosability of Star Graphs,” Computers Electrical Eng., vol. 22, no. 1, pp. 37-44, 1996.
[19] 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.
[20] S. Khanna and W.K. Fuchs, “A Linear Time Algorithm for Sequential Diagnosis in Hypercubes,” J. Parallel and Distributed Computing, vol. 26, pp. 38-53, 1995.
[21] 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.
[22] C. Kime, “System Diagnosis,” Fault-Tolerant Computing: Theory and Techniques, D.K. Pradhan, ed. vol. II, Chapter 8, Englewood Cliffs, N.J.: Prentice Hall, 1986.
[23] 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, pp. 1064-1069, Aug. 2004.
[24] 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.
[25] F.P. Preparata, G. Metze, and R.T. Chien, “On the Connection Assignment Problem of Diagnosable Systems,” IEEE Trans. Electronic Computers, vol. 16, pp. 848-854, 1967.
[26] Y. Saad and M.H. Schultz, “Topological Properties of Hypercubes,” IEEE Trans. Computers, vol. 37, no 7, pp. 867-872, July 1988.
[27] A. Sengupta and A.T. Danbura, “On Self-Diagnosable Multiprocessor Systems: Diagnosis by the Comparison Approach,” IEEE Trans. Computers, vol. 41, no. 11, pp. 1386-1396, Nov. 1992.
[28] 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.
[29] D. Wang, “Diagnosability of Enhanced Hypercubes,” IEEE Trans. Computers, vol. 43, no. 9, pp. 1054-1061, Sept. 1994.
[30] 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.

Index Terms:
Index Terms- Diagnosability, matching composition network, multiprocessor system, PMC model, precise diagnosis strategy, sequential diagnosis, (t,k){\hbox{-}}{\rm diagnosis}.
Citation:
Guey-Yun Chang, Gen-Huey Chen, Gerard J. Chang, "(t,k)-Diagnosis for Matching Composition Networks," IEEE Transactions on Computers, vol. 55, no. 1, pp. 88-92, Jan. 2006, doi:10.1109/TC.2006.1