Efficient Embeddings of Trees in Hypercubes

The boolean hypercube is a particularly versatile network for parallel computing. It is well known that multidimensional grid machines can be simulated on a hypercube with no communications overhead. In this paper it is shown that every bounded-degree tree can be simulated on the hypercube with constant communications overhead. In fact, the proof shows that every bounded-degree graph with an O(1)-separator can be embedded in a hypercube of the same size with dilation and congestion both O(1). It is also proved that not all bounded-degree graphs can be efficiently embedded within the hypercube. 1. Introduction. The binary hypercube is emerging as one of the most popular network architectures for parallel machines. This is due partly to the facts that the hypercube has a simple recursive structure and that there are simple algorithms for message routing on the hypercube that work well in practice. Another important consideration in the choice of network architecture is its ability to accommodate different algorithms efficiently. The problem of efficiently implementing various algorithms on parallel architectures has traditionally been studied as the