Embedding Large Mesh of Trees and Related Networks in the Hypercube with Load Balancing

The ability to embed arbitrarily large graphs in smaller graphs has important applications in mapping problems which require more processors than is available in a parallel architecture. We address this problem with the main focus on balancing processor loads. We show that maximum level of system utilization can be obtained when each host node emulates an equal number of "busy" guest nodes for each step of computation. While the embedding methods used are applicable to a variety of guest graphs, the main focus of the paper is on meshes of tree due to their importance as parallel architectures. Methods are also developed for embedding arbitrarily large complete binary trees and grids.