## Abstract

(t,k)-Diagnosis, which is a generalization of sequential diagnosis, requires that at least k faulty processors be identified and repaired in each iteration when there are at most t faulty processors, where t ≥ k. Based on the assumption that each vertex is adjacent to at least one fault-free vertex, the conditional (t,k)-diagnosis of graphs was investigated by using the comparison diagnosis model. Lower bounds on the conditional (t, k)-diagnosability of graphs were derived, and applied to obtain the following results. 1) Symmetric d-dimensional grids are conditionally (N/2d+1 - 1,2d - 1)-diagnosable when d ≥ 2 and N (the number of vertices)≥ 4^{d}. 2) Symmetric d-dimensional tori are conditionally (1/5(N + min{8/5 N2/3, 2N-20/15} - 2),6)-diagnosable when d = 2 and N ≥ 49 and (N/2d+1 - 1,4d - 2)-diagnosable when d ≥ 3 and N ≥ 4^{d}. 3) Cube-connected cycles are conditionally (N/4 - 1, 4)-diagnosable. 4) k-ary trees are conditionally (N/k+1 - 1, 1)-diagnosable.

Original language | English |
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Article number | 6871331 |

Pages (from-to) | 1622-1632 |

Number of pages | 11 |

Journal | IEEE Transactions on Computers |

Volume | 64 |

Issue number | 6 |

DOIs | |

State | Published - 1 Jun 2015 |

## Keywords

- (t,k)-diagnosis
- Conditional fault diagnosis
- MM∗ model
- fault-tolerance
- multiprocessor systems
- sequential diagnosis
- system-level diagnosis