### Abstract

We obtain the fault diameter of k-ary n-cube interconnection networks (also known as n-dimensional k-torus networks). We start by constructing a complete set of node-disjoint paths (i.e., as many paths as the degree) between any two nodes of a k-ary n-cube. Each of the obtained paths is of length zero, two, or four plus the minimum length except for one path in a special case (when the Hamming distance between the two nodes is one) where the increase over the minimum length may attain eight. These results improve those obtained in [8] where the length of some of the paths has a variable increase (which can be arbitrarily large) over the minimum length. These results are then used to derive the fault diameter of the k-ary n-cube, which is shown to be Δ + 1 where Δ is the fault free diameter.

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

Pages (from-to) | 903-907 |

Number of pages | 5 |

Journal | IEEE Transactions on Parallel and Distributed Systems |

Volume | 8 |

Issue number | 9 |

DOIs | |

Publication status | Published - 1997 |

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### Keywords

- Fault diameter
- Interconnection networks
- K-ary n-cube
- Node-disjoint paths
- Torus

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Theoretical Computer Science
- Computational Theory and Mathematics

### Cite this

*IEEE Transactions on Parallel and Distributed Systems*,

*8*(9), 903-907. https://doi.org/10.1109/71.615436

**Fault diameter of k-ary n-cube networks.** / Day, Khaled; Al-Ayyoub, Abdel Elah.

Research output: Contribution to journal › Article

*IEEE Transactions on Parallel and Distributed Systems*, vol. 8, no. 9, pp. 903-907. https://doi.org/10.1109/71.615436

}

TY - JOUR

T1 - Fault diameter of k-ary n-cube networks

AU - Day, Khaled

AU - Al-Ayyoub, Abdel Elah

PY - 1997

Y1 - 1997

N2 - We obtain the fault diameter of k-ary n-cube interconnection networks (also known as n-dimensional k-torus networks). We start by constructing a complete set of node-disjoint paths (i.e., as many paths as the degree) between any two nodes of a k-ary n-cube. Each of the obtained paths is of length zero, two, or four plus the minimum length except for one path in a special case (when the Hamming distance between the two nodes is one) where the increase over the minimum length may attain eight. These results improve those obtained in [8] where the length of some of the paths has a variable increase (which can be arbitrarily large) over the minimum length. These results are then used to derive the fault diameter of the k-ary n-cube, which is shown to be Δ + 1 where Δ is the fault free diameter.

AB - We obtain the fault diameter of k-ary n-cube interconnection networks (also known as n-dimensional k-torus networks). We start by constructing a complete set of node-disjoint paths (i.e., as many paths as the degree) between any two nodes of a k-ary n-cube. Each of the obtained paths is of length zero, two, or four plus the minimum length except for one path in a special case (when the Hamming distance between the two nodes is one) where the increase over the minimum length may attain eight. These results improve those obtained in [8] where the length of some of the paths has a variable increase (which can be arbitrarily large) over the minimum length. These results are then used to derive the fault diameter of the k-ary n-cube, which is shown to be Δ + 1 where Δ is the fault free diameter.

KW - Fault diameter

KW - Interconnection networks

KW - K-ary n-cube

KW - Node-disjoint paths

KW - Torus

UR - http://www.scopus.com/inward/record.url?scp=0031236740&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031236740&partnerID=8YFLogxK

U2 - 10.1109/71.615436

DO - 10.1109/71.615436

M3 - Article

VL - 8

SP - 903

EP - 907

JO - IEEE Transactions on Parallel and Distributed Systems

JF - IEEE Transactions on Parallel and Distributed Systems

SN - 1045-9219

IS - 9

ER -