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On the computational complexity of routing in faulty k-ary n-cubes and hypercubes. (2012)
Journal Article
Stewart, I. (2012). On the computational complexity of routing in faulty k-ary n-cubes and hypercubes. Parallel Processing Letters, 22(1), Article 1250003. https://doi.org/10.1142/s012962641250003x

We equate a routing algorithm in a (faulty) interconnection network whose underlying graph is a k-ary n-cube or a hypercube, that attempts to route a packet from a fixed source node to a fixed destination node, with the sub-digraph of (healthy) links... Read More about On the computational complexity of routing in faulty k-ary n-cubes and hypercubes..

Node-to-node disjoint paths in k-ary n-cubes with faulty edges. (2012)
Conference Proceeding
Xiang, Y., Stewart, I., & Madelaine, F. (2012). Node-to-node disjoint paths in k-ary n-cubes with faulty edges. In 2011 IEEE 17th International Conference on Parallel and Distributed Systems (ICPADS 2011). Proceedings of a meeting held 7-9 December 2011, Tainan, Taiwan (181-187). https://doi.org/10.1109/icpads.2011.85

Let u and v be any two given nodes in a k-ary n-cube Qnk with at most 2n-2 faulty edges. Suppose that the number of healthy links incident with u is no more than that of v, and denote this number by m. In this paper, we show that there are m mutually... Read More about Node-to-node disjoint paths in k-ary n-cubes with faulty edges..