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Products of Networks with Logarithmic Diameter and Fixed Degree
September 1995 (vol. 6 no. 9)
pp. 963-975

Abstract—This paper first analyzes some general properties of product networks pertinent to parallel architectures and then focuses on three case studies. These are products of complete binary trees, shuffle-exchange, and de Bruijn networks. It is shown that all of these are powerful architectures for parallel computation, as evidenced by their ability to efficiently emulate numerous other architectures. In particular, r-dimensional grids, and r-dimensional meshes of trees can be embedded efficiently in products of these graphs, i.e. either as a subgraph or with small constant dilation and congestion. In addition, the shuffle-exchange network can be embedded in r-dimensional product of shuffle exchange networks with dilation cost 2r and congestion cost 2. Similarly, the de Bruijn network can be embedded in r-dimensional product of de Bruijn networks with dilation cost r and congestion cost 4. Moreover, it is well known that shuffle-exchange and de Bruijn graphs can emulate the hypercube with a small constant slowdown for “normal” algorithms. This means that their product versions can also emulate these hypercube algorithms with constant slowdown. Conclusions include a discussion of many open research areas.

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Index Terms:
Product networks, interconnection networks, parallel architectures, multiprocessors, graph embedding, application specific array processors, emulation, embedded architectures.
Citation:
Kemal Efe, Antonio Fernández, "Products of Networks with Logarithmic Diameter and Fixed Degree," IEEE Transactions on Parallel and Distributed Systems, vol. 6, no. 9, pp. 963-975, Sept. 1995, doi:10.1109/71.466633
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