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<p>We study hypercube networks with a very large number of faulty nodes. A simple and natural condition, the <it>local subcube-connectivity</it>, is identified under which hypercube networks with a very large number of faulty nodes still remain connected. The condition of local subcube-connectivity can be detected and maintained in a distributed manner based on localized management. Efficient routing algorithms on locally subcube-connected hypercube networks are developed. Our algorithms are distributed and local-information-based in the sense that each node in the network knows only its neighbors' status and no global information of the network is required by the algorithms. For a locally subcube-connected hypercube network that may contain up to 37.5 percent faulty nodes, our algorithms run in linear time and, for any two given nonfaulty nodes, find a routing path of length bounded by four times the Hamming distance between the two nodes. Theoretical analysis and experimental results are presented which show that, under a variety of probability distributions of node failures, hypercube networks are locally subcube-connected with a very high probability and our routing algorithms run in linear time and construct routing paths of nearly optimal length.</p>
Interconnection network, hypercube, routing algorithm, fault tolerance

J. Chen, G. Wang and S. Chen, "Locally Subcube-Connected Hypercube Networks: Theoretical Analysis and Experimental Results," in IEEE Transactions on Computers, vol. 51, no. , pp. 530-540, 2002.
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