On the Area of Hypercube Layouts

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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 N² 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).