Multiple Network Embedding into Hybercubes

In this paper we present solutions to the problem of how to efficiently embed r guest networks Go,. . . , G,.-l, r k, into a it-dimensional hypercube H so that every processor of H is assigned at most r guest processors. The guest networks considered include complete binary trees, leap trees, linear arrays, and meshes. 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 guest network. We consider two models of load distribution. An embedding has a balanced load distribution if no two of the r p r e cessors assigned to a processor of H come from the same guest network, and it has an unbalanced load distribution otherwise. For the case when all Gi's are complete binary trees, we show the following result: in the balanced load model r complete binary trees can be embedded into H with an optimal dilation of2 and a congestion of 5. For the unbalanced load model we use a different strategy and achieve a congestion of 2 while keeping the dilation at 2. Our results for the other types of networks are of a similar nature.