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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-17514-5_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17513-8
Online ISBN: 978-3-642-17514-5
eBook Packages: Computer ScienceComputer Science (R0)