Abstract
A number of hypercube-variant networks attempt to improve the hypercube by adding extra connections and thus reducing the diameter of the constructed network. We briefly outline a model which describes these variant networks. Further, we show that by restricting this model, we can describe hypercube variants with exactly the same number of edges as the hypercube. We mention several such networks which all have diameter about n/2. We describe a new network within this class that has diameter about 2n/5, thus improving the best known previous bound by a constant factor. We show that within a limited construction paradigm our network is best possible.
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Cull, P., Larson, S.M. Smaller diameters in hypercube-variant networks. Telecommunication Systems 10, 175–184 (1998). https://doi.org/10.1023/A:1019167000458
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DOI: https://doi.org/10.1023/A:1019167000458