Embedding complete binary trees in product graphs

Abstract

This paper shows how to embed complete binary trees in products of complete binary trees, products of shuffle-exchange graphs, and products of de Bruijn graphs. The main emphasis of the embedding methods presented here is how to emulate arbitrarily large complete binary trees in these product graphs with low slowdown. For the embedding methods presented here the size of the host graph can be fixed to an arbitrary size, while we define no bound on the size of the guest graph. This is motivated by the fact that the host architecture has a fixed number of processors due to its physical design, while the guest graph can grow arbitrarily large depending on the application. The results of this paper widen the class of computations that can be performed on these product graphs which are often cited as being low-cost alternatives for hypercubes.