Abstract
(t,k)-Diagnosis, which is a generalization of sequential diagnosis, requires that at least k faulty processors should be identified and repaired in each iteration provided there are at most t faulty processors, where t ≥ k. Let κ(G) and n(G) be the node connectivity and the number of nodes in G, respectively. We show that the class of m-dimensional component-composition graphs G for m ≥ 4 is (Ω(h),κ(G))-diagnosable, where \(h=\frac{2^{m-2}\times \lg{(m-1)}}{m-1}\) if 2m − 1 ≤ n(G) < m!; and h = 2m − 2 if n(G) ≥ m!. Based on this result, the (t,k)-diagnosability of numerous multiprocessor systems can be computed efficiently.
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References
Akers, S.B., Horel, D., Krishnamurthy, B.: The star graph: an attractive alternative to the n-cube. In: Proceedings of the International Conference on Parallel Processing, pp. 393–400 (1987)
Akers, S.B., Krishnamurthy, B.: A group-theoretic model for symmetric interconnection networks. IEEE Transactions on Computers 38(4), 555–566 (1989)
Araki, T., Shibata, Y.: (t,k)-diagnosable system: A generalization of the PMC models. IEEE Transactions on Computers 52(7), 971–975 (2003)
Armstrong, J.R., Gray, F.G.: Fault diagnosis in a boolean n-cube array of microprocessors. IEEE Transactions on Computers C-30(8), 587–590 (1981)
Chang, G.Y., Chen, G.H.: (t,k)-diagnosability of multiprocessor systems with applications to grids and tori. SIAM Journal on Computing 37(4), 1280–1298 (2007)
Chang, G.Y., Chen, G.H., Chang, G.J.: (t,k)-diagnosis for matching composition networks. IEEE Transactions on Computers 55(1), 88–92 (2006)
Chang, G.Y., Chen, G.H., Chang, G.J.: (t,k)-diagnosis for matching composition networks under the MM* model. IEEE Transactions on Computers 56(1), 73–79 (2007)
Esfahanian, A.H., Ni, L.M., Sagan, B.E.: The twisted n-cube with application to multiprocessing. IEEE Transactions on Computers 40(1), 88–93 (1991)
Fan, J.: Diagnosability of crossed cubes under the comparison diagnosis model. IEEE Transactions on Parallel and Distributed Systems 13(7), 687–692 (2002)
Jwo, J.S., Lakshmivarahan, S., Dhall, S.K.: A new class of interconnection networks based on the alternating group. Networks 23, 315–326 (1993)
Kaneko, K., Sawada, N.: An algorithm for node-to-set disjoint paths problem in burnt pancake graphs. IEICE Transactions on Information and Systems E86VD(12), 2588–2594 (2003)
Kaneko, K., Sawada, N.: An algorithm for node-to-node disjoint paths problem in burnt pancake graphs. IEICE Transactions on Information and Systems E90VD(1), 306–313 (2007)
Lakshmivarahan, S., Jwo, J.S., Dhall, S.K.: Symmetry in interconnection networks based on cayley graphs of permutation groups: a survey. Parallel Computing 19(4), 361–407 (1993)
Park, J.H., Kim, H.C., Lim, H.S.: Many-to-many disjoint path covers in hypercube-like interconnection networks with faulty elements. IEEE Transactions on Parallel and Distributed Systems 17(3), 227–240 (2006)
Park, J.H., Lim, H.S., Kim, H.C.: Panconnectivity and pancyclicity of hypercube-like interconnection networks with faulty elements. Theortical Computer Science 377, 170–180 (2007)
Preparata, F.P., Metze, G., Chien, R.T.: On the connection assignment problem of diagnosable systems. IEEE Transactions on Electronic Computers EC-16(6), 848–854 (1967)
Suzuki, Y., Kaneko, K.: An algorithm for node-disjoint paths in pancake graphs. IEICE Transactions on Information and Systems E86-D(3), 610–615 (2003)
Vaidya, A.S., Rao, P.S.N., Shankar, S.R.: A class of hypercube-like networks. In: Proc. 5th Symp. on Parallel and Distributed Processing, pp. 800–803 (1993)
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Hsieh, SY., Chen, CA. (2010). Computing the (t,k)-Diagnosability of Component-Composition Graphs and Its Application. In: Cheong, O., Chwa, KY., Park, K. (eds) Algorithms and Computation. ISAAC 2010. Lecture Notes in Computer Science, vol 6507. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17514-5_31
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DOI: https://doi.org/10.1007/978-3-642-17514-5_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17513-8
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