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<p><b>Abstract</b>—The WK-recursive networks own two structural advantages: expansibility and equal degree. A network is <it>expansible</it> if no changes to node configuration and link connection are necessary when it is expanded, and of <it>equal degree</it> if its nodes have the same degree no matter what the size is. However, the number of nodes contained in a WK-recursive network is restricted to <it>d</it><super><it>t</it></super>, where <it>d</it> > 1 is the size of the basic building block and <it>t</it>≥ 1 is the level of expansion. The incomplete WK-recursive networks, which were proposed to relieve this restriction, are allowed to contain an arbitrary number of basic building blocks, while preserving the advantages of the WK-recursive networks.</p><p>Designing shortest-path routing algorithms for incomplete networks is in general more difficult than for complete networks. The reason is that most incomplete networks lack a unified representation. One of the contributions of this paper is to demonstrate a useful representation, i.e., the multistage graph representation, for the incomplete WK-recursive networks. On the basis of it, a shortest-path routing algorithm is then proposed. With <it>O</it>(<it>d</it>·<it>t</it>) time preprocessing, this algorithm takes <it>O</it>(<it>t</it>) time for each intermediate node to determine the next node along the shortest path.</p>
Graph-theoretic interconnection network, incomplete WK-recursive network, multistage graph representation, routing, shortest-path routing algorithm, WK-recursive network.

D. Duh, G. Chen and M. Su, "A Shortest-Path Routing Algorithm for Incomplete WK-Recursive Networks," in IEEE Transactions on Parallel & Distributed Systems, vol. 8, no. , pp. 367-379, 1997.
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