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The Partial Line Digraph Technique in the Design of Large Interconnection Networks
July 1992 (vol. 41 no. 7)
pp. 848-857

The following problem arises in the design of some interconnection networks for distributed systems. Namely, to construct digraphs with given maximum out-degree, reduced diameter, easy routing, good connectivity, and good expandability. To this end, a method based on the concept of partial line digraph is presented. This proposal, which turns out to be a generalization of the so-called line digraph technique, allows digraphs that satisfy all the above-mentioned requirements to be obtained. In particular, it is shown that the partial line digraphs of Kautz digraphs solve the (d, N) digraph problem, i.e. to minimize the diameter D in a digraph of maximum out-degree d and number of vertices N, for any N in the range d/sup D-1/+d/sup D-2/+. . .+1>or=N>or=d/sup D/+d/sup D-1/.

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Index Terms:
partial line digraph technique; design; large interconnection networks; distributed systems; maximum out-degree; routing; connectivity; expandability; Kautz digraphs; directed graphs; multiprocessor interconnection networks.
M.A. Fiol, A.S. Llado, "The Partial Line Digraph Technique in the Design of Large Interconnection Networks," IEEE Transactions on Computers, vol. 41, no. 7, pp. 848-857, July 1992, doi:10.1109/12.256453
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