Embeddings in hypercubes

Authors:
Marilynn Livingston;Quentin F. Stout
Affiliations:
Department of Electrical Engineering and Computer Science University of Michigan Ann Arbor, MI 48109-2122 USA;Department of Electrical Engineering and Computer Science University of Michigan Ann Arbor, MI 48109-2122 USA
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
1988

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Abstract

One important aspect of efficient use of a hypercube computer to solve a given problem is the assignment of subtasks to processors in such a way that the communication overhead is low. The subtasks and their inter-communication requirements can be modeled by a graph, and the assignment of subtasks to processors viewed as an embedding of the task graph into the graph of the hypercube network. We survey the known results concerning such embeddings, including expansion/dilation tradeoffs for general graphs, embeddings of meshes and trees, packings of multiple copies of a graph, the complexity of finding good embeddings, and critical graphs which are minimal with respect to some property. In addition, we describe several open problems.