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 \(k,l \in {I \mkern-6mu N}\), k ≥ 8, such that \(\displaystyle \frac{5}{3} + c_k < \frac{l}{k} \leq 2\), \(\displaystyle c_k=\frac{4k+3}{3 \cdot 2^{\rule[-3pt]{0mm}{0mm}2/3 k}}\), thus improving known results. Our embedding technique also leads to improved dilation 1 embeddings in the case \(\displaystyle \frac{3}{2} < \frac{l}{k} \leq \frac{5}{3}+c_k\).
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Klasing, R. (1998). Improved Compressions of Cube-Connected Cycles Networks. In: Hromkovič, J., Sýkora, O. (eds) Graph-Theoretic Concepts in Computer Science. WG 1998. Lecture Notes in Computer Science, vol 1517. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10692760_20
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DOI: https://doi.org/10.1007/10692760_20
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