Embedding Hierarchical Fibonacci Cubes In Faulty Hierarchic Cubic Networks

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

Ali Karcı

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

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

Kaynakça

• [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.