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Issue No.09 - September (2005 vol.16)

pp: 853-865

Jung-Sheng Fu , IEEE

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TPDS.2005.109

ABSTRACT

<p><b>Abstract</b>—Recently, the WK-recursive network has received much attention due to its many favorable properties such as a high degree of scalability. By <tmath>K(d,t)</tmath>, we denote the WK-recursive network of level <tmath>t</tmath>, each of whose basic modules is a <tmath>d{\hbox{-}}{\rm{node}}</tmath> complete graph, where <tmath>d>1</tmath> and <tmath>t \geq 1</tmath>. In this paper, we first show that <tmath>K(d, t)</tmath> is Hamiltonian-connected, where <tmath>d\geq 4</tmath>. 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 <tmath>K(d, t)</tmath> with at most <tmath>d-3</tmath> faulty nodes, where <tmath>d\geq 4</tmath>. Since the connectivity of <tmath>K(d, t)</tmath> is <tmath>d-1</tmath>, the result is optimal.</p>

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 & Distributed Systems*, vol.16, no. 9, pp. 853-865, September 2005, doi:10.1109/TPDS.2005.109