Issue No. 12 - December (2011 vol. 60)

ISSN: 0018-9340

pp: 1704-1717

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TC.2010.201

Chun-An Chen , National Cheng Kung University, Tainan

Sun-Yuan Hsieh , National Cheng Kung University, Tainan

ABSTRACT

(t,k)-Diagnosis, which is a generalization of sequential diagnosis, requires that at least k faulty processors be identified and replaced in each iteration provided there are at most t faulty processors, where t \ge k. Let \kappa (G) and n(G) be, respectively, the node connectivity and the number of nodes in a graph G. In this paper, we compute the (t,k)-diagnosability for a class of component-composition graphs under the comparison diagnosis model. We show that the m-dimensional component-composition graph G (m \ge 4) is (\Omega (h),\kappa (G))-diagnosable, where h= \left\{\matrix{\displaystyle{2^{m-2}\times (m-3)\times \lg {(m-1)}\over (m-1)^2} & {\rm if} 2^{m-1} \le n(G) < m!\cr {\displaystyle 2^{m-2}\times (m-3)\over m-1}\hfill & {\rm if} n(G) \ge m!.\hfill}\right. Based on this result, the (t,k)-diagnosability of several multiprocessor systems, including hypercubes, crossed cubes, twisted cubes, locally twisted cubes, multiply twisted cubes, generalized twisted cubes, recursive circulants, Möbius cubes, Mcubes, star graphs, bubble-sort graphs, pancake graphs, and burnt pancake graphs, can be computed efficiently.

INDEX TERMS

Comparison diagnosis model, component-composition graphs, the MM* model, (t, k)-diagnosis, (t, k)-diagnosability.

CITATION

Chun-An Chen, Sun-Yuan Hsieh, "(t,k)-Diagnosis for Component-Composition Graphs under the MM* Model",

*IEEE Transactions on Computers*, vol. 60, no. , pp. 1704-1717, December 2011, doi:10.1109/TC.2010.201