### Abstract

This paper presents a new fault-tolerant routing algorithm for the binary n-cube which overcomes the limitations of the recently-proposed safety vectors algorithm (IEEE Trans. Parallel Distribut. Syst. 9 (4) (1998) 321). The algorithm is based on the concept of "unsafety vectors". Each node A starts by computing a first level unsafety set, S_{1}
^{A}, composed of the set of unreachable neighbours. It then performs (m - 1) exchanges with its neighbours to determine the k-level unsafety set, S_{k}
^{A}, for all 1 ≤ k ≤ m, where m is an adjustable parameter between 1 and n. S_{k}
^{A} represents the set of all nodes at Hamming distance k from node A which are faulty or unreachable from A due to faulty nodes (or links). Equipped with these unsafety sets, each node calculates unsafety vectors, which are then used to achieve an efficient fault-tolerant routing in the binary n-cube. The kth element of the unsafety vector of node A represents a measure of the routing unsafety at distance k from A. We present an analytical study proving some properties of the proposed algorithm. We also conduct a comparative analysis through extensive simulation experiments that reveal the superiority of the proposed algorithm over the safety vectors algorithm (IEEE Trans. Parallel Distribut. Syst. 9 (4) (1998) 321) in terms of different performance measures, e.g. routing distances and percentage of reachability.

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

Pages (from-to) | 783-793 |

Number of pages | 11 |

Journal | Journal of Systems Architecture |

Volume | 47 |

Issue number | 9 |

DOIs | |

Publication status | Published - Mar 2002 |

### Fingerprint

### Keywords

- Fault-tolerant routing
- Hypercube
- Interconnection networks
- Multicomputers
- Performance evaluation
- Safety vectors

### ASJC Scopus subject areas

- Hardware and Architecture
- Software

### Cite this

**Unsafety vectors : A new fault-tolerant routing for the binary n-cube.** / Al-Sadi, J.; Day, K.; Ould-Khaoua, M.

Research output: Contribution to journal › Article

*Journal of Systems Architecture*, vol. 47, no. 9, pp. 783-793. https://doi.org/10.1016/S1383-7621(01)00031-5

}

TY - JOUR

T1 - Unsafety vectors

T2 - A new fault-tolerant routing for the binary n-cube

AU - Al-Sadi, J.

AU - Day, K.

AU - Ould-Khaoua, M.

PY - 2002/3

Y1 - 2002/3

N2 - This paper presents a new fault-tolerant routing algorithm for the binary n-cube which overcomes the limitations of the recently-proposed safety vectors algorithm (IEEE Trans. Parallel Distribut. Syst. 9 (4) (1998) 321). The algorithm is based on the concept of "unsafety vectors". Each node A starts by computing a first level unsafety set, S1 A, composed of the set of unreachable neighbours. It then performs (m - 1) exchanges with its neighbours to determine the k-level unsafety set, Sk A, for all 1 ≤ k ≤ m, where m is an adjustable parameter between 1 and n. Sk A represents the set of all nodes at Hamming distance k from node A which are faulty or unreachable from A due to faulty nodes (or links). Equipped with these unsafety sets, each node calculates unsafety vectors, which are then used to achieve an efficient fault-tolerant routing in the binary n-cube. The kth element of the unsafety vector of node A represents a measure of the routing unsafety at distance k from A. We present an analytical study proving some properties of the proposed algorithm. We also conduct a comparative analysis through extensive simulation experiments that reveal the superiority of the proposed algorithm over the safety vectors algorithm (IEEE Trans. Parallel Distribut. Syst. 9 (4) (1998) 321) in terms of different performance measures, e.g. routing distances and percentage of reachability.

AB - This paper presents a new fault-tolerant routing algorithm for the binary n-cube which overcomes the limitations of the recently-proposed safety vectors algorithm (IEEE Trans. Parallel Distribut. Syst. 9 (4) (1998) 321). The algorithm is based on the concept of "unsafety vectors". Each node A starts by computing a first level unsafety set, S1 A, composed of the set of unreachable neighbours. It then performs (m - 1) exchanges with its neighbours to determine the k-level unsafety set, Sk A, for all 1 ≤ k ≤ m, where m is an adjustable parameter between 1 and n. Sk A represents the set of all nodes at Hamming distance k from node A which are faulty or unreachable from A due to faulty nodes (or links). Equipped with these unsafety sets, each node calculates unsafety vectors, which are then used to achieve an efficient fault-tolerant routing in the binary n-cube. The kth element of the unsafety vector of node A represents a measure of the routing unsafety at distance k from A. We present an analytical study proving some properties of the proposed algorithm. We also conduct a comparative analysis through extensive simulation experiments that reveal the superiority of the proposed algorithm over the safety vectors algorithm (IEEE Trans. Parallel Distribut. Syst. 9 (4) (1998) 321) in terms of different performance measures, e.g. routing distances and percentage of reachability.

KW - Fault-tolerant routing

KW - Hypercube

KW - Interconnection networks

KW - Multicomputers

KW - Performance evaluation

KW - Safety vectors

UR - http://www.scopus.com/inward/record.url?scp=0036496443&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036496443&partnerID=8YFLogxK

U2 - 10.1016/S1383-7621(01)00031-5

DO - 10.1016/S1383-7621(01)00031-5

M3 - Article

VL - 47

SP - 783

EP - 793

JO - Journal of Systems Architecture

JF - Journal of Systems Architecture

SN - 1383-7621

IS - 9

ER -