Abstract
Trees are a common structure to represent the intertask communication pattern of a parallel algorithm. In this paper, we consider the embedding of 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-2k embedding of a level-(p + k) binary tree, into an n-dimensional star graph, where and k is any positive integer. The first result offers a tree of size comparable or superior to existing results, but with less congestion and dilation. The second result provides more flexibility in the embeddable tree sizes compared to existing results. © 1999 John Wiley & Sons, Inc. Networks 33: 221–231, 1999
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