On the area of hypercube layouts

Authors:
Ronald I. Greenberg;Lee Guan
Affiliations:
Department of Mathematical and Computer Sciences, Loyola University, 6525 N. Sheridan Rd., Chicago, IL;Acecomm Corporation, 704 Quince Orchard Rd., Gaithersburg, MD
Venue:
Information Processing Letters
Year:
2002

Citing 11
Cited 2

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The congestion of n-cube layout on a rectangular grid

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WG '93 Proceedings of the 19th International Workshop on Graph-Theoretic Concepts in Computer Science
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Mesh-of-trees and alternative interconnection networks for single-chip parallelism

IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Layout volumes of the hypercube

GD'04 Proceedings of the 12th international conference on Graph Drawing

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Abstract

This paper precisely analyzes the wire density and required area in standard layout styles for the hypercube. It shows that the most natural, regular layout of a hypercube of N2 nodes in the plane, in an N × N grid arrangement, uses [2N/3] + 1 horizontal wiring tracks for each row of nodes. (In the process, we see that the number of tracks per row can be reduced by 1 with a less regular design, as can also be seen from an independent argument of Bezrukov et al.) 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).