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Improved Compressions of Cube-Connected Cycles Networks
August 1998 (vol. 9 no. 8)
pp. 803-812

Abstract—We present a new technique for the embedding of large cube-connected cycles networks (CCC) into smaller ones, a problem that arises when algorithms designed for an architecture of an ideal size are to be executed on an existing architecture of a fixed size. Using the new embedding strategy, we show that the CCC of dimension l can be embedded into the CCC of dimension k with dilation 1 and optimum load for any k, $l \in {\hbox{\sl{\rlap{N}\kern1.5pt{\hbox{N}}}}},$k≥ 8, such ${\textstyle{5 \over 3}}+c_k<{\textstyle{l \over k}}\le 2,$$c_k={\textstyle{{4k +3} \over {3\cdot 2^{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3}k}}}},$ thus improving known results. Our embedding technique also leads to improved dilation-1 embeddings in the case ${\textstyle{3 \over 2}}<{\textstyle{l \over k}}\le {\textstyle{5 \over 3}}+c_k.$

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Index Terms:
Parallel computations, parallel architectures, interconnection networks, graph embedding, network simulation, cube-connected cycles network.
Ralf Klasing, "Improved Compressions of Cube-Connected Cycles Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 9, no. 8, pp. 803-812, Aug. 1998, doi:10.1109/71.706051
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