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Issue No.02 - February (2005 vol.54)

pp: 176-184

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TC.2005.33

ABSTRACT

Processor fault diagnosis takes an important role in fault-tolerant computing on multiprocessor systems. There are two classical diagnosis strategies—the precise strategy and the pessimistic strategy, both of which are based on the well-known PMC diagnostic model. Nevertheless, the degree of diagnosability of the system is limited under these two strategies. A better method, called the t/k-diagnosis strategy, is proposed by Somani and Peleg, in which the identified fault-set is allowed to contain at most k fault-free processors. Using this diagnosis strategy, the degree of diagnosability of the hypercube increases greatly as the number of the fault-free processors in the fault-set increases. In this paper, we study the t/k-diagnosability of so-called BC graphs that include hypercubes, crossed cubes, Möbius cubes, and twisted cubes, etc. We show that any n-dimensional BC graph is t(n,k)/k-diagnosable when n\geq 4 and 0\leq k\leq n, where t(n,k)=(k+1)n-{\frac{1}{2}}(k+1)(k+2)+1. Therefore, the crossed cube, the Möbius cube, and the twisted cube all have the same t/k-diagnosability as the hypercube. As a result, the algorithms developed for diagnosis on the hypercube may also be used to diagnose multiprocessor systems whose network topologies are based on BC graphs.

INDEX TERMS

Diagnosis, diagnosability, precise diagnosis strategy, pessimistic diagnosis strategy, t/k-diagnosis strategy, BC graph, hypercube, crossed cube, Möbius cube, twisted cube.

CITATION

Jianxi Fan, Xiaola Lin, "The t/k-Diagnosability of the BC Graphs",

*IEEE Transactions on Computers*, vol.54, no. 2, pp. 176-184, February 2005, doi:10.1109/TC.2005.33