On the Area of Hypercube Layouts

Details On the Area of Hypercube Layouts On the Area of Hypercube Layouts

2001-05-29

arxiv.org/abs/cs/0105034v1

condensed and revised in Information Processing Letters, v. 84, n. 1, pp. 41--46, Sep. 2002

Computer Science

Distributed, Parallel, and Cluster Computing

8 pages, 4 figures, LaTeX

Scientific paper

This paper precisely analyzes the wire density and required area in standard layout styles for the hypercube. The most natural, regular layout of a hypercube of N^2 nodes in the plane, in a N x N grid arrangement, uses floor(2N/3)+1 horizontal wiring tracks for each row of nodes. (The number of tracks per row can be reduced by 1 with a less regular design.) This paper also gives a simple formula for the wire density at any cut position and a full characterization of all places where the wire density is maximized (which does not occur at the bisection).

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