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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. 713718, June, 1993.  
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@article{ 10.1109/71.242151, author = {S.B. Tien and C.S. Raghavendra}, title = {Algorithms and Bounds for Shortest Paths and Diameter in Faulty Hypercubes}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {4}, number = {6}, issn = {10459219}, year = {1993}, pages = {713718}, doi = {http://doi.ieeecomputersociety.org/10.1109/71.242151}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Parallel and Distributed Systems TI  Algorithms and Bounds for Shortest Paths and Diameter in Faulty Hypercubes IS  6 SN  10459219 SP713 EP718 EPD  713718 A1  S.B. Tien, A1  C.S. Raghavendra, PY  1993 KW  Index Termsbounds; shortest paths; faulty hypercubes; ndimensional hypercube; complexity;diameter; computational complexity; fault tolerant computing; hypercube networks;parallel algorithms VL  4 JA  IEEE Transactions on Parallel and Distributed Systems ER   
In an ndimensional hypercube Qn, with the fault set mod F mod >2/sub n2/, 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 QnF, when mod F mod >2/sub n2/, 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 >2n2, 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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