Incomplete Hypercubes: Embeddings of Tree-Related Networks

Abstract

We consider the incomplete hypercubes, a generalization of the binary hypercube networks in the sense that the number of nodes can be arbitrary as opposed to a strict power of 2. The capability of the incomplete hypercubes to execute parallel programs is studied here using graph embedding techniques. We show optimal (or nearly optimal) embeddings of various guest networks such as X-trees, full-ringed binary trees, tree machines, mesh of trees, and pyramids into the optimum-sized incomplete hypercube host.