Locally subcube-connected hypercube networks: theoretical analysis and experimental results

We study hypercube networks with a very large number of faulty nodes. A simple and natural condition, the local subcube-connectivity, 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.