Embedding Meshes into the Star - Connectedcycles Interconnection

The star-connected cycles (SCC) graph was recently proposed as an attractive interconnection network for parallel processing, using a star graph to connect cycles of nodes. This paper presents embeddings of p-dimensional meshes into an n-dimensional SCC graph (1 p n), which have load 1, expansion 1, and dilation ranging from 1 to 3 + 2b(n ? 1)=2c + 2bn=4c (the dilation varies among mesh dimensions). We show that, despite the fact that the dilation of our embeddings increases with n, a small communication slowdown can be obtained if high-bandwidth links are used within the cycles of the SCC graph.