Publication 1996 Issue No. 12 - December Abstract - On Parallel Algorithms for Single-Fault Diagnosis in Fault Propagation Graph Systems
On Parallel Algorithms for Single-Fault Diagnosis in Fault Propagation Graph Systems
December 1996 (vol. 7 no. 12)
pp. 1217-1223
 ASCII Text x Nageswara S.V. Rao, "On Parallel Algorithms for Single-Fault Diagnosis in Fault Propagation Graph Systems," IEEE Transactions on Parallel and Distributed Systems, vol. 7, no. 12, pp. 1217-1223, December, 1996.
 BibTex x @article{ 10.1109/71.553268,author = {Nageswara S.V. Rao},title = {On Parallel Algorithms for Single-Fault Diagnosis in Fault Propagation Graph Systems},journal ={IEEE Transactions on Parallel and Distributed Systems},volume = {7},number = {12},issn = {1045-9219},year = {1996},pages = {1217-1223},doi = {http://doi.ieeecomputersociety.org/10.1109/71.553268},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on Parallel and Distributed SystemsTI - On Parallel Algorithms for Single-Fault Diagnosis in Fault Propagation Graph SystemsIS - 12SN - 1045-9219SP1217EP1223EPD - 1217-1223A1 - Nageswara S.V. Rao, PY - 1996KW - Fault diagnosisKW - single faultKW - fault propagation graphKW - operative diagnosisKW - CREW PRAMKW - and hypercube.VL - 7JA - IEEE Transactions on Parallel and Distributed SystemsER -

Abstract—Systems modeled as directed graphs where nodes represent components and edges represent fault propagation between components, are studied from a parallel computation viewpoint. Some of the components are equipped with alarms that ring in response to an abnormal condition. The single fault diagnosis problem is to compute the set of all potential failure sources, PS, that correspond to a set of ringing alarms AR. There is a lower bound of Ω(e + k(nk + 1)) for any sequential algorithm for this problem (under a decision tree model), where n and e are the number of nodes and edges of the graph respectively, and k is the number of alarms. Using a CREW PRAM of $p\le {{{k(n-k+1)} \over {\log k}}}$ processors, the graph can be preprocessed in O(n2.81 / p + log2n) time; then PS can be computed in O(k(nk + 1) / p + log k) time. On a hypercube of $p\le {{{k(n-k+1)} \over {\log k}}}$ processors, the preprocessing can be done in $O\left( {{{{n^2} \over {\sqrt p}}}+{{{n^{2.61}} \over {p^{0.805}}}} +{{{nk(n-k+1)} \over p}}} \right)$ time; then PS can be computed in $O\left( {{{{k(n-k+1)\log n} \over {p\log k}}}+\log n} \right)$ time.

[1] K.H. Abbott, "Robust Operative Diagnosis as Problem Solving in a Hypothesis Space," Proc. Seventh Nat'l Conf. Artificial Inteligence.,St. Paul, Minn., 1988.
[2] M. Abramovici, M.A. Breuer, and A.D. Friedman, Digital Systems Testing and Testable Design.New York: Computer Science Press, 1990.
[3] S.G. Akl, The Design and Analysis of Parallel Algorithms. Orlando, Fl.: Academic Press, 1989.
[4] D. Allemang, M.C. Tanner, T. Bylander, and J. Josephson, "Computational Complexity of Hypothesis Assembly, Proc. Tenth Int'l Joint Conf. Artificial Intelligence, pp. 1,112-1,117,Milan, 1987.
[5] F. Barsi, F. Grandoni, and P. Maestrini, "A Theory of Diagnosability Without Repairs," IEEE Trans. Computers., vol. 25, pp. 585-593, 1976.
[6] D.M. Blough and A. Pelc, "Complexity of Fault Diagnosis in Comparison Models," IEEE Trans. Computers, vol. 41, pp. 318-324, 1992.
[7] R.P. Brent, "The Parallel Evaluation of General Arithmetic Expressions," J. ACM, vol. 21, pp. 201-206, 1974.
[8] A.K. Chandra, "Maximal Parallelism in Matrix Multiplication," IBM Research Report, RC 6193, 1976.
[9] D. Chester, D. Lamb, and P. Dhurjati, "Rule-Based Computer Alarm Analysis in Chemical Process Plants," Proc. Micon-delcn., vol. 22, pp. 22-29, 1984.
[10] F.Y. Chin, J. Lam, and I. Chen, "Efficient Parallel Algorithms for Some Graph Problems," Comm. ACM, vol. 25, no. 9, pp. 659-665, 1982.
[11] R. Cole and U. Vishkin, "Approximate Parallel Scheduling. Part 1: The Basic Technique with Applications to Optimal Parallel List Ranking in Logarithmic Time," SIAM J. Computing, vol. 18, pp. 128-142, 1988.
[12] E. Dekel, D. Nassimi, and S. Sahni, "Parallel Matrix and Graph Algorithms," SIAM J. Computing, vol. 10, no. 4, pp. 657-675, 1981.
[13] M.C. Er, "A Parallel Computation Approach to Topological Sorting," The Computer J., vol. 26, no. 4, pp. 293-295, 1983.
[14] J.P. Fishburn and R. Finkel, "Quotient Networks," IEEE Trans. Computers, pp. 288-295, 1982.
[15] H. Fujiwara, Logic Testing and Design for Testability. MIT Press, 1985.
[16] D.S. Hirschberg, A.K. Chandra, and D.V. Sarwate, "Computing Connected Components on Parallel Computers," Comm. ACM, vol. 22, no. 8, pp. 461-464, 1979.
[17] M. Ira, K. Aoki, E. O'Shima, and H. Matsuyama, "An Algorithm for Diagnosis of System Failures in the Chemical Process," Comp. Chem. Eng., vol. 3, pp. 489-493, 1985.
[18] M. Kokawa, S. Miyazaki, and S. Shingai, "Fault Location Using Digraph and Inverse Direction Search with Applications," Automatica, vol. 19, no. 6, pp. 729-735, 1983.
[19] H. Nakano and Y. Nakanishi, "Graph Representation and Diagnosis for Multiunit Faults," IEEE Trans. Reliability, vol. 23, no. 5, pp. 320-325, 1974.
[20] S. Padalkar, G. Karsai, C. Biegl, J. Sztipanovits, K. Okuda, and N. Miyasaka, "Real-Time Fault Diagnosis," IEEE Expert, pp. 75-85, June 1991.
[21] D.K. Pradhan, "Dynamically Restructurable Fault-Tolerant Processor Network Architectures," IEEE Trans. Computers, vol. 34, no. 5, pp. 434-440, 1985.
[22] F.P. Preparata, G. Metze, and R.T. Chien, "On the Connection Assignment Problem of Diagnosable Systems," IEEE Trans. Electronic Computing, vol. 16, pp. 848-954, 1967.
[23] N.S.V. Rao, "Expected-Value Analysis of Two Single Fault Diagnosis Algorithms," IEEE Trans. Computers, vol. 42, no. 3, pp. 272-280, 1993.
[24] N.S.V. Rao, "Computational Complexity Issues in Operative Diagnosis of Graph-Based Systems," IEEE Trans. Computers, vol. 42, no. 4, pp. 447-457, 1993.
[25] N.S.V. Rao and N. Viswanadham, "Fault Diagnosis in Dynamical Systems: A Graph Theoretic Approach," Int'l J. Systems Science, vol. 18, no. 4, pp. 687-695, 1987.
[26] K.W. Ryu and J. JaJa, "List ranking on the Hypercube," Proc. 1989 Int'l Conf. Parallel Processing, vol. III, pp. 20-23, 1989.
[27] M.R. Samatham and D.K. Pradhan, "The de Bruijn Multiprocessor Network: A Versatile Parallel Processing and Sorting Network for VLSI," IEEE Trans. Computers, vol. 38, no. 4, pp. 567-581, Apr. 1989.
[28] C. L. Seitz,“The cosmic cube,”CACM, vol. 28, pp. 22–33, Jan. 1985.
[29] J. Shiozaki, H. Matsuyama, E. O'Shima, and M. Ira, "An Improved Algorithm for Diagnosis of System Failures in the Chemical Process," Comp. Chem. Eng., vol. 9, no. 3, pp. 285-293, 1985.
[30] A.K. Somani, D. Avis, and V.K. Agarwal, "On Complexity of Single-Fault Diagnosability and Diagnosis Problems," IEEE Trans. Computers, vol. 38, pp. 195-201, 1989.
[31] S. Toida, "A Graph Model for Fault Diagnosis," J. Digital Systems, vol. VI, no. 4, pp. 345-365, 1982.
[32] R.E. Tarjan, "Depth-First Search and Linear Graph Algorithms," SIAM J. Computing, vol. 1, no. 2, pp. 146-160, 1972.
[33] N.H. Ulerich and G.J. Powers, "Online Hazard Aversion and Fault Diagnosis in Chemical Processes: The Digraph + Fault-Tree Method," IEEE Trans. Reliability, vol. 37, no. 2, pp. 171-177, 1988.

Index Terms:
Fault diagnosis, single fault, fault propagation graph, operative diagnosis, CREW PRAM, and hypercube.
Citation:
Nageswara S.V. Rao, "On Parallel Algorithms for Single-Fault Diagnosis in Fault Propagation Graph Systems," IEEE Transactions on Parallel and Distributed Systems, vol. 7, no. 12, pp. 1217-1223, Dec. 1996, doi:10.1109/71.553268