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Hamiltonicity of the WK-Recursive Network with and without Faulty Nodes
September 2005 (vol. 16 no. 9)
pp. 853-865

Abstract—Recently, the WK-recursive network has received much attention due to its many favorable properties such as a high degree of scalability. By K(d,t), we denote the WK-recursive network of level t, each of whose basic modules is a d{\hbox{-}}{\rm{node}} complete graph, where d>1 and t \geq 1. In this paper, we first show that K(d, t) is Hamiltonian-connected, where d\geq 4. A network is Hamiltonian-connected if it contains a Hamiltonian path between every two distinct nodes. In other words, a Hamiltonian-connected network can embed the longest linear array between any two distinct nodes with dilation, congestion, load, and expansion all equal to one. Then, we construct fault-free Hamiltonian cycles in K(d, t) with at most d-3 faulty nodes, where d\geq 4. Since the connectivity of K(d, t) is d-1, the result is optimal.

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Index Terms:
WK-recursive, embedding, Hamiltonian-connected, interconnection network, fault-tolerant embedding, Hamiltonian cycle.
Citation:
Jung-Sheng Fu, "Hamiltonicity of the WK-Recursive Network with and without Faulty Nodes," IEEE Transactions on Parallel and Distributed Systems, vol. 16, no. 9, pp. 853-865, Sept. 2005, doi:10.1109/TPDS.2005.109
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