Issue No. 06 - June (2013 vol. 62)

ISSN: 0018-9340

pp: 1097-1110

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TC.2012.58

Sun-Yuan Hsieh , National Cheng Kung University, Tainan

Chun-An Chen , National Cheng Kung University, Tainan

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 $(t\ge k)$. In this paper, we propose a unified approach for computing the $((t,k))$-diagnosability of numerous multiprocessor systems (graphs) under the Preparata, Metze, and Chien's model, 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. Our approach first sketches the common properties of the above classes of graphs, and defines a superclass of graphs, called $(m)$--dimensional component-composition graphs, to cover them. We then show that the $(m)$-dimensional component-composition graph $(G)$ for $(m \ge 4)$ is $((\Omega (h),\kappa (G)))$-diagnosable, where $(\displaystyle h={\left\{\matrix{{2^{m-2}\times \lg {(m-1)}\over m-1} &{\rm if} 2^{m-1} \le \vert V(G)\vert < m!\cr 2^{m-2}\hfill & {\rm if} \vert V(G)\vert \ge m!,\hfill}\right.})$ and $(\kappa (G))$ and $(\vert V(G)\vert)$ denote the node connectivity and the number of nodes in $(G)$, respectively. Based on this result, the $((t,k))$-diagnosability of the above multiprocessor systems can be computed efficiently.

INDEX TERMS

Multiprocessing systems, Fault diagnosis, Computational modeling, Sequential diagnosis, Program processors, Maintenance engineering, Hypercubes, k))$--diagnosis, Diagnosability, component-composition graphs, graph theory, multiprocessor systems, the PMC model, $((t

CITATION

Sun-Yuan Hsieh, Chun-An Chen, "Component-Composition Graphs: (t,k)-Diagnosability and Its Application",

*IEEE Transactions on Computers*, vol. 62, no. , pp. 1097-1110, June 2013, doi:10.1109/TC.2012.58