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

• Published in: IEEE transactions on computers Vol. 51; no. 5; pp. 530 - 540
• Main Authors: Chen, Jianer, Wang, Guojun, Chen, Songqiao
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.05.2002; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Computer networks; Construction; Hypercubes; Management; Networks; Optimization; Routing (telecommunications); Studies
• ISSN: 0018-9340; 1557-9956
• DOI: 10.1109/TC.2002.1004592

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.