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The partial line digraph technique in the design of large interconnection networks

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2 Author(s)
M. A. Fiol ; Departament de Matematica Aplicada i Telematica, Univ. Politecnica de Catalunya, Barcelona, Spain ; A. S. Llado

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 dD-1+dD-2+. . .+1⩽N⩽dD+dD-1

Published in:

IEEE Transactions on Computers  (Volume:41 ,  Issue: 7 )