Improved Bound for Dilation of an Embedding onto Circulant Networks
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Implementation of parallel algorithms and simulation of different interconnection networks need an effective tool, that is, graph embedding. This paper focuses on improving a lower bound obtained in Rajan et al. (Comput J 58:3271–3278, 2015) for dilation of an embedding onto circulant networks. In addition, this paper provides algorithms to compute dilation of embedding circulant network into certain trees, for instance, m-rooted complete binary tree, m-rooted sibling tree, and r-dimensional hypertree, proving that the improved bound obtained is sharp.
KeywordsEmbedding Dilation Circulant network Binary tree Sibling tree Hypertree
Mathematics Subject Classification05C60 05C85
The work of R. Sundara Rajan was partially supported by Project No. ECR/2016/1993, Science and Engineering Research Board (SERB), Department of Science and Technology (DST), Government of India.
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