Assignment of tasks to parallel architectures

This paper discusses the use of certain types of parallel contractions, combined with graph embeddings, to efficiently map task graphs into networks of processing elements (PEs). The problem addressed is the case when the relation between the network graph H and the task graph G is |V(G)|>|V(H)|, or even |V(G )|>>|V(H)|. In such cases it is not sufficient to use only graph embedding techniques. The authors propose the use of graph contractions to supplement graph embedding techniques in three possible forms. In the first case, the task graph G is contracted to G´, then G´ is embedded into H. In the second case, the task graph G is first embedded into a graph H´, followed by a contraction of H´ to some known topology H. In the third case, G is contracted to H by a topology transferring contraction, i.e., the contraction maps the topology of G into the topology of H . The authors give formal definitions of contractions. They review the properties which make certain contractions more desirable than others and survey some recent results of parallel contractions for rings, full binary trees, grids, hypercubes and cube-connected cycles