### Abstract

(t, k)-Diagnosis, which is a generalization of sequential diagnosis, requires that at least t faulty processors be identified and replaced in each iteration provided there are at most t faulty processors, where t ≥ k. Let κ(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 ≥ 4) is (Ω(h),κ(G))-diagnosable, where h= 2^{m-1} × (m ^{-3}) × lg(m^{-1}) (m^{-1})/(m^{-1}) ^{2} if 2^{m-2} ≤ n(G)<; m 2^{m-1} × (m-3)/m^{-1} if n(G) ≥ m!. 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, Mobius cubes, Mcubes, star graphs, bubble-sort graphs, pancake graphs, and burnt pancake graphs, can be computed efficiently.

Original language | English |
---|---|

Article number | 5601693 |

Pages (from-to) | 1704-1717 |

Number of pages | 14 |

Journal | IEEE Transactions on Computers |

Volume | 60 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2011 Dec 1 |

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### All Science Journal Classification (ASJC) codes

- Software
- Theoretical Computer Science
- Hardware and Architecture
- Computational Theory and Mathematics

### Cite this

*IEEE Transactions on Computers*,

*60*(12), 1704-1717. [5601693]. https://doi.org/10.1109/TC.2010.201

}

*IEEE Transactions on Computers*, vol. 60, no. 12, 5601693, pp. 1704-1717. https://doi.org/10.1109/TC.2010.201

**(t,k)-diagnosis for component-composition graphs under the MM* model.** / Chen, Chun An; Hsieh, Sun-Yuan.

Research output: Contribution to journal › Article

TY - JOUR

T1 - (t,k)-diagnosis for component-composition graphs under the MM* model

AU - Chen, Chun An

AU - Hsieh, Sun-Yuan

PY - 2011/12/1

Y1 - 2011/12/1

N2 - (t, k)-Diagnosis, which is a generalization of sequential diagnosis, requires that at least t faulty processors be identified and replaced in each iteration provided there are at most t faulty processors, where t ≥ k. Let κ(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 ≥ 4) is (Ω(h),κ(G))-diagnosable, where h= 2m-1 × (m -3) × lg(m-1) (m-1)/(m-1) 2 if 2m-2 ≤ n(G)<; m 2m-1 × (m-3)/m-1 if n(G) ≥ m!. 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, Mobius cubes, Mcubes, star graphs, bubble-sort graphs, pancake graphs, and burnt pancake graphs, can be computed efficiently.

AB - (t, k)-Diagnosis, which is a generalization of sequential diagnosis, requires that at least t faulty processors be identified and replaced in each iteration provided there are at most t faulty processors, where t ≥ k. Let κ(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 ≥ 4) is (Ω(h),κ(G))-diagnosable, where h= 2m-1 × (m -3) × lg(m-1) (m-1)/(m-1) 2 if 2m-2 ≤ n(G)<; m 2m-1 × (m-3)/m-1 if n(G) ≥ m!. 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, Mobius cubes, Mcubes, star graphs, bubble-sort graphs, pancake graphs, and burnt pancake graphs, can be computed efficiently.

UR - http://www.scopus.com/inward/record.url?scp=84873465914&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84873465914&partnerID=8YFLogxK

U2 - 10.1109/TC.2010.201

DO - 10.1109/TC.2010.201

M3 - Article

AN - SCOPUS:84873465914

VL - 60

SP - 1704

EP - 1717

JO - IEEE Transactions on Computers

JF - IEEE Transactions on Computers

SN - 0018-9340

IS - 12

M1 - 5601693

ER -