Computer Science Technical Reports
CS at VT

Graph Embeddings and Simplicial Maps

Heath, Lenwood S. (1993) Graph Embeddings and Simplicial Maps. Technical Report TR-93-40, Computer Science, Virginia Polytechnic Institute and State University.

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An undirected graph is viewed as a simplicial complex. The notion of a graph embedding of a guest graph in a host graph is generalized to the realm of simplicial maps. Dilation is redefined in this more general setting. Lower bounds on dilation for various guest and host graphs are considered. Of particular interest are graphs that have been proposed as communication networks for parallel architectures. Bhatt et al. provide a lower bound on dilation for embedding a planar guest graph in a butterfly host graph. Here, this lower bound is extended in two directions. First, a lower bound that applies to arbitrary guest graphs is derived, using tools from algebraic topology. Second, this lower bound is shown to apply to arbitrary host graphs through a new graph-theoretic measure, called bidecomposability. Bounds on the bidecomposability of the butterfly graph and of the k-dimensional torus are determined. As corollaries to the main lower bound theorem, lower bounds are derived for embedding arbitrary planar graphs, genus g graphs, and k-dimensional meshes in a butterfly host graph.

Item Type:Departmental Technical Report
Subjects:Computer Science > Historical Collection(Till Dec 2001)
ID Code:382
Deposited By:User autouser
Deposited On:05 December 2001