Embedding of congestion-free complete binary trees with dilation two in star graphs

Trees are a common structure to represent the inter-task communication pattern of a parallel algorithm. In this paper, we consider the problem of embedding a complete binary tree in a star graph with the objective of minimizing congestion and dilation. We develop a congestion-free, dilation-2, load-1 embedding of a level-p binary tree into an n-dimensional star graph, where p=Σ_i=2ⁿ [log i] and k is any positive integer. The result offers a tree of size comparable or superior to existing results, but with less congestion and dilation