Multiple Network Embedding into Hybercubes

Abstract

Abstract In this paper we consider the problem of embedding r guest networks G0, ..., Gr−1, into a k-dimensional hypercube H so that every processor of H is assigned at most r guest processors and dilation and congestion are minimized. Network G, can be a complete binary tree, a leap tree, a linear array, or a mesh. We show that r such guest networks can simultaneously be embedded into H without a significant increase in dilation and congestion compared to the embedding of a single network when r ≤ k. For r > k, the increase in the cost measures is proportional to r/k. We consider two models which differ in the requirements imposed on the r guest processors assigned to a processor of H.