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Algorithms and Bounds for Shortest Paths and Diameter in Faulty Hypercubes
June 1993 (vol. 4 no. 6)
pp. 713-718

In an n-dimensional hypercube Qn, with the fault set mod F mod >2/sub n-2/, assuming Sand D are not isolated, it is shown that there exists a path of length equal to at mosttheir Hamming distance plus 4. An algorithm with complexity O( mod F mod logn) is given to find such a path. A bound for the diameter of the faulty hypercube Qn-F, when mod F mod >2/sub n-2/, as n+2 is obtained. This improves the previously known bound of n+6 obtained by A.-H. Esfahanian (1989). Worst case scenarios are constructed to show that these bounds for shortest paths and diameter are tight. It is also shown that when mod F mod >2n-2, the diameter bound is reduced to n+1 if every node has at least 2 nonfaulty neighbors and reduced to n if every node has at least 3 nonfaulty neighbors.

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Index Terms:
Index Termsbounds; shortest paths; faulty hypercubes; n-dimensional hypercube; complexity;diameter; computational complexity; fault tolerant computing; hypercube networks;parallel algorithms
S.B. Tien, C.S. Raghavendra, "Algorithms and Bounds for Shortest Paths and Diameter in Faulty Hypercubes," IEEE Transactions on Parallel and Distributed Systems, vol. 4, no. 6, pp. 713-718, June 1993, doi:10.1109/71.242151
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