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Issue No.12 - December (1999 vol.10)
pp: 1290-1298
ABSTRACT
<p><b>Abstract</b>—In this paper, we first show that the <it>degree four Cayley graph</it> proposed in a paper appearing in the January 1996 issue of <it>IEEE Transactions on Parallel and Distributed Systems</it> is indeed isomorphic to the <it>wrapped butterfly</it>. The isomorphism was first reported by Muga and Wei in the proceedings of PDPTA "96.The isomorphism is shown by using an edge-preserving bijective mapping. Due to the isomorphism, algorithms for the degree four Cayley graph can be easily developed in terms of wrapped butterfly and topological properties of one network can be easily derived in terms of the other. Next, we present the first optimal oblivious one-to-one permutation routing scheme for these networks in terms of the wrapped butterfly. Our algorithm runs in time <tmath>$O(\sqrt{N})$</tmath>, where <tmath>$N$</tmath> is the network size.</p>
INDEX TERMS
Cayley graph, wrapped butterfly, isomorphism, permutation routing.
CITATION
David S.L. Wei, Felix P. Muga, Kshirasagar Naik, "Isomorphism of Degree Four Cayley Graph and Wrapped Butterfly and Their Optimal Permutation Routing Algorithm", IEEE Transactions on Parallel & Distributed Systems, vol.10, no. 12, pp. 1290-1298, December 1999, doi:10.1109/71.819950
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