A New Efficient Algorithm for Embedding an Arbitrary Binary Tree into Its Optimal Hypercube

Thed-dimensional binary hypercube is a very popular model of parallel computation. On the other hand, the execution of many algorithms can be represented by binary trees, making it desirable to simulate binary trees on a hypercube. In this paper, we present a simple one-to-one embedding of arbitrary binary trees into their optimal hypercubes with dilation 8 and constant node-congestion. The novelty of our method is the use of an intermediate quadtree data structure, which also permits the embedding to be efficiently computed on the hypercube itself.