Araştırma Makalesi

Yıl 2016,
Cilt: 1 Sayı: 1, 14 - 19, 01.12.2016
### Öz

## Hierarchical Fibonacci Cubes HFC(n+2) can be

obtained from the Hierarchic Cubic Network HCN(n,n) by removing certain nodes

and edges. This problem is very simple when no faulty node exists in an

HCN(n,n), however, it becomes very sophisticated if some faulty nodes appear in

an HCN(n,n). In this paper, we tried to distinguish HFC(n+2) in faulty

HCN(n,n), and it can also be considered as a fault-tolerant embedding in

HCN(n,n). Then, we shall show how to dierctly embed a HFC(n+2) into a faulty

HCN(n,n) and prove that if no more than two clusters which contain faulty

nodes, then HFC(n+2) can be directly embedded. Another case is that if there

are more than two clusters which contain faulty nodes, then the labels of

faulty nodes must be (I_{i},K) and (I_{i},L) for each cluster.

### Anahtar Kelimeler

### Kaynakça

obtained from the Hierarchic Cubic Network HCN(n,n) by removing certain nodes

and edges. This problem is very simple when no faulty node exists in an

HCN(n,n), however, it becomes very sophisticated if some faulty nodes appear in

an HCN(n,n). In this paper, we tried to distinguish HFC(n+2) in faulty

HCN(n,n), and it can also be considered as a fault-tolerant embedding in

HCN(n,n). Then, we shall show how to dierctly embed a HFC(n+2) into a faulty

HCN(n,n) and prove that if no more than two clusters which contain faulty

nodes, then HFC(n+2) can be directly embedded. Another case is that if there

are more than two clusters which contain faulty nodes, then the labels of

faulty nodes must be (I

Hierarchical Cubic Network - HCN(n n) Hierarchical Fibonacci Cube – HFC(n)

- [1] K. Chose, and K. R. Desai, “Hierarchical Cubic Networks”, IEEE Transactions on Parallel and Distributed Systems, vol. 6, pp.427-435, 1995.
- [2] W.-J. Hsu, “Fibonacci Cubes – A New Interconnection Topology”, IEEE Transactions on Parallel and Distributed Systems, vol. 4, pp. 3-12, 1993.
- [3] W.K. Chiang and R.J.Chen, “Topological properties of hierarchical cubic networks, J. of systems architecture, v.42, pp:289-307, 1996.
- [4] A. Karci, “New Interconnection Netwroks: Fibonacci Cube and Extended Fibonacci Cubes Based Hierarchic Networks”, IEEE: The 15th International Conference on Information Networking (ICOIN-15), Jan. 31 - Feb. 2, 2001, Beppu Convention(B-Con) Plaza, Beppu City, Japan.
- [5] A. Karci, “Recursive Construction of Hierarchical Fibonacci Cubes and Hierarchical Extended Fibonacci Cubes”, IEEE: 2001 International Conference on Parallel and Distributed Systems (ICPADS-2001), June 26-29, 2001, KyongJu city, Korea.
- [6] S.K. Yun, K.H. Park, “Comments on hierarchical cubic networks”, IEEE trans. On Parallel and Distributed systems, v.9, n.4, pp:410-414, 1998.
- [7] F.-S. Jiang, S.-J. Horng, and T.-W. Kao, “Embedding of Generalized Fibonacci Cubes in Hypercubes with Faulty Nodes”, IEEE. Trans. on Parallel and Distributed Systems, vol:8, pp: 727-737, 1997.
- [8] K. Efe, “Embedding Mesh of Trees in the Hypercubes”, J. of Parallel and Distributed Computing, vol:11, pp:222-230, 1991.

Yıl 2016,
Cilt: 1 Sayı: 1, 14 - 19, 01.12.2016
### Öz

## Hierarchical Fibonacci Cubes HFC(n+2) can be

obtained from the Hierarchic Cubic Network HCN(n,n) by removing certain nodes

and edges. This problem is very simple when no faulty node exists in an

HCN(n,n), however, it becomes very sophisticated if some faulty nodes appear in

an HCN(n,n). In this paper, we tried to distinguish HFC(n+2) in faulty

HCN(n,n), and it can also be considered as a fault-tolerant embedding in

HCN(n,n). Then, we shall show how to dierctly embed a HFC(n+2) into a faulty

HCN(n,n) and prove that if no more than two clusters which contain faulty

nodes, then HFC(n+2) can be directly embedded. Another case is that if there

are more than two clusters which contain faulty nodes, then the labels of

faulty nodes must be (I_{i},K) and (I_{i},L) for each cluster.

### Anahtar Kelimeler

### Kaynakça

obtained from the Hierarchic Cubic Network HCN(n,n) by removing certain nodes

and edges. This problem is very simple when no faulty node exists in an

HCN(n,n), however, it becomes very sophisticated if some faulty nodes appear in

an HCN(n,n). In this paper, we tried to distinguish HFC(n+2) in faulty

HCN(n,n), and it can also be considered as a fault-tolerant embedding in

HCN(n,n). Then, we shall show how to dierctly embed a HFC(n+2) into a faulty

HCN(n,n) and prove that if no more than two clusters which contain faulty

nodes, then HFC(n+2) can be directly embedded. Another case is that if there

are more than two clusters which contain faulty nodes, then the labels of

faulty nodes must be (I

Hierarchical Cubic Network - HCN(n n) Hierarchical Fibonacci Cube – HFC(n)

- [1] K. Chose, and K. R. Desai, “Hierarchical Cubic Networks”, IEEE Transactions on Parallel and Distributed Systems, vol. 6, pp.427-435, 1995.
- [2] W.-J. Hsu, “Fibonacci Cubes – A New Interconnection Topology”, IEEE Transactions on Parallel and Distributed Systems, vol. 4, pp. 3-12, 1993.
- [3] W.K. Chiang and R.J.Chen, “Topological properties of hierarchical cubic networks, J. of systems architecture, v.42, pp:289-307, 1996.
- [4] A. Karci, “New Interconnection Netwroks: Fibonacci Cube and Extended Fibonacci Cubes Based Hierarchic Networks”, IEEE: The 15th International Conference on Information Networking (ICOIN-15), Jan. 31 - Feb. 2, 2001, Beppu Convention(B-Con) Plaza, Beppu City, Japan.
- [5] A. Karci, “Recursive Construction of Hierarchical Fibonacci Cubes and Hierarchical Extended Fibonacci Cubes”, IEEE: 2001 International Conference on Parallel and Distributed Systems (ICPADS-2001), June 26-29, 2001, KyongJu city, Korea.
- [6] S.K. Yun, K.H. Park, “Comments on hierarchical cubic networks”, IEEE trans. On Parallel and Distributed systems, v.9, n.4, pp:410-414, 1998.
- [7] F.-S. Jiang, S.-J. Horng, and T.-W. Kao, “Embedding of Generalized Fibonacci Cubes in Hypercubes with Faulty Nodes”, IEEE. Trans. on Parallel and Distributed Systems, vol:8, pp: 727-737, 1997.
- [8] K. Efe, “Embedding Mesh of Trees in the Hypercubes”, J. of Parallel and Distributed Computing, vol:11, pp:222-230, 1991.

Toplam 8 adet kaynakça vardır.

Konular | Bilgisayar Yazılımı |
---|---|

Bölüm | PAPERS |

Yazarlar | |

Yayımlanma Tarihi | 1 Aralık 2016 |

Gönderilme Tarihi | 20 Ekim 2016 |

Kabul Tarihi | 24 Kasım 2016 |

Yayımlandığı Sayı | Yıl 2016 Cilt: 1 Sayı: 1 |

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