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A shortest-path routing algorithm for incomplete WK-recursive networks
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DOI：10.1109/71.588608.png)
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摘要
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The WK-recursive networks own two structural advantages: expansibility and equal degree. A network is expansible if no changes to node configuration and link connection are necessary when it is expanded, and of equal degree 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 d(t) where d > 1 is the size of the basic building block and t greater than or equal to 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. Designing shortest-path routing algorithms ion 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 O(d . t) time preprocessing, this algorithm lakes O(t) time for each intermediate node to determine the next node along the shortest path.
Keyword:
graph-theoretic interconnection network
incomplete WK-recursive network
multistage graph representation
routing
shortest-path routing algorithm
WK-recursive network
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