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Issue No.08 - August (1998 vol.9)
pp: 803-812
ABSTRACT
<p><b>Abstract</b>—We present a new technique for the embedding of large cube-connected cycles networks (<it>CCC</it>) 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 <it>CCC</it> of dimension <it>l</it> can be embedded into the <it>CCC</it> of dimension <it>k</it> with <it>dilation</it> 1 and optimum <it>load</it> for any <it>k</it>, <tmath>$l \in {\hbox{\sl{\rlap{N}\kern1.5pt{\hbox{N}}}}},$</tmath><it>k</it>≥ 8, such <tmath>${\textstyle{5 \over 3}}+c_k<{\textstyle{l \over k}}\le 2,$</tmath><tmath>$c_k={\textstyle{{4k +3} \over {3\cdot 2^{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3}k}}}},$</tmath> thus improving known results. Our embedding technique also leads to improved dilation-1 embeddings in the case <tmath>${\textstyle{3 \over 2}}<{\textstyle{l \over k}}\le {\textstyle{5 \over 3}}+c_k.$</tmath></p>
INDEX TERMS
Parallel computations, parallel architectures, interconnection networks, graph embedding, network simulation, cube-connected cycles network.
CITATION
Ralf Klasing, "Improved Compressions of Cube-Connected Cycles Networks", IEEE Transactions on Parallel & Distributed Systems, vol.9, no. 8, pp. 803-812, August 1998, doi:10.1109/71.706051
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