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On the Longest Fault-Free Paths in Hypercubes with More Faulty Nodes

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4 Author(s)
Tz-Liang Kueng ; Dept. of Comput. Sci., Nat. Chiao Tung Univ., Hsinchu ; Liang, T. ; Tan, J.J.M. ; Lih-Hsing Hsu

Faults in a network may take various forms such as hardware/software errors, node/link faults, etc. In this paper, node-faults are addressed. Let F be a faulty set of f les 2n - 6 conditional node-faults in an injured n-cube Qn such that every node of Qn still has at least two fault - free neighbors. Then we show that Qn - F contains a path of length at least 2n - 2f - 1 (respectively, 2n - 2f - 2) between any two nodes of odd (respectively, even) distance. Since an n-cube is a bipartite graph, such kind of the fault- free path turns out to be the longest one in the case when all faulty nodes belong to the same partite set.

Published in:

Parallel Architectures, Algorithms, and Networks, 2008. I-SPAN 2008. International Symposium on

Date of Conference:

7-9 May 2008