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Longest Fault-Free Paths in Hypercubes with both Faulty Nodes and Edges

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3 Author(s)
Sun-Yuan Hsieh ; Nat. Cheng Kung Univ., Tainan ; Che-Nan Kuo ; Hui-Ling Huang

The hypercube is one of the most versatile and efficient interconnection networks for parallel computation. Let Fv (respectively, Fe) be the set of faulty vertices (respectively, faulty edges) in an n-dimensional hypercube Qn. In this paper, we show that Qn - Fv - Fe contains a fault free path with length at least 2n - 2|Fv| - 1(or 2n - 2|Fv| - 2) between two arbitrary vertices of odd (or even) distance if |Fv| + |Fe| les n - 2, where n ges 3. Since Qn is bipartite of equal-size partite sets, the path is longest in the worst case. Furthermore, since Qn is regular of vertex-degree n, both the number of faults tolerated and the length of a longest fault-free path obtained are worst-case optimal.

Published in:

Future Generation Communication and Networking (FGCN 2007)  (Volume:2 )

Date of Conference:

6-8 Dec. 2007