Congestion-free, dilation-2 embedding of complete binary trees into star graphs

Trees are a common structure to represent the inter-task communication pattern of a parallel algorithm. In this paper, we consider the embedding a complete binary tree in a star graph with the objective of minimizing congestion and dilation. We develop two embeddings: i) a congestion-free, dilation-2, load-1 embedding of a level-p binary tree, and ii) a congestion-free, dilation-2, load-2 k embedding of a level-(p+k) binary tree, into an n-dimensional star graph, where p = n i=2 blog ic = (n log n) and k is any positive integer. The rst result ooers a tree of size comparable or superior to existing results, but with less congestion and dilation. The second result provides more exibility in the embeddable tree sizes compared to existing results.