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On the Area of Hypercube Layouts

Ronald I. Greenberg·Lee Guan
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Abstract

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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Ronald I. Greenberg, Lee Guan. 2001-05-29. On the Area of Hypercube Layouts. https://arxiv.org/abs/cs/0105034

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