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OPTIMAL EMBEDDING OF HONEYCOMB NETWORKS INTO HYPERCUBES
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We present an optimal embedding of a honeycomb network (honeycomb mesh and honeycomb torus) of size n into a hypercube with expansion ratio of [Formula: see text] when n is a power of two. When n is not a power of two, the expansion is [Formula: see text], which we conjecture to be near optimal. For a honeycomb mesh, the dilation of the embedding is 1. For a honeycomb torus, the dilation can be as large as 2ā log nā+3, because of the extra links connecting symmetric opposite nodes of degree two. A honeycomb network, built recursively using hexagon tessellation, is a multiprocessor interconnection network, and also a Cayley graph, and it is better than the planar mesh with the same number of nodes in terms of degree, diameter, number of links, and bisection width.
World Scientific Pub Co Pte Lt
Title: OPTIMAL EMBEDDING OF HONEYCOMB NETWORKS INTO HYPERCUBES
Description:
We present an optimal embedding of a honeycomb network (honeycomb mesh and honeycomb torus) of size n into a hypercube with expansion ratio of [Formula: see text] when n is a power of two.
When n is not a power of two, the expansion is [Formula: see text], which we conjecture to be near optimal.
For a honeycomb mesh, the dilation of the embedding is 1.
For a honeycomb torus, the dilation can be as large as 2ā log nā+3, because of the extra links connecting symmetric opposite nodes of degree two.
A honeycomb network, built recursively using hexagon tessellation, is a multiprocessor interconnection network, and also a Cayley graph, and it is better than the planar mesh with the same number of nodes in terms of degree, diameter, number of links, and bisection width.
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