Conditional (t,k)-Diagnosis in graphs by using the comparison diagnosis model

Chun An Chen, Guey Yun Chang, Sun Yuan Hsieh

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9 Scopus citations


(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)≥ 4d. 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 ≥ 4d. 3) Cube-connected cycles are conditionally (N/4 - 1, 4)-diagnosable. 4) k-ary trees are conditionally (N/k+1 - 1, 1)-diagnosable.

Original languageEnglish
Article number6871331
Pages (from-to)1622-1632
Number of pages11
JournalIEEE Transactions on Computers
Issue number6
StatePublished - 1 Jun 2015


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


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