Three dimensional circuit layouts
SIAM Journal on Computing
Three-Dimensional VLSI: a case study
Journal of the ACM (JACM)
Area-Efficient VLSI Layouts for Binary Hypercubes
IEEE Transactions on Computers
The congestion of n-cube layout on a rectangular grid
Discrete Mathematics - Special issue on Selected Topics in Discrete Mathematics conferences
Optimal three-dimensional layout of interconnection networks
Theoretical Computer Science
On the area of hypercube layouts
Information Processing Letters
Two Algorithms for Three Dimensional Orthogonal Graph Drawing
GD '96 Proceedings of the Symposium on Graph Drawing
Three-Dimensional Orthogonal Graph Drawing with Optimal Volume
GD '00 Proceedings of the 8th International Symposium on Graph Drawing
Efficient VLSI Layouts of Hypercubic Networks
FRONTIERS '99 Proceedings of the The 7th Symposium on the Frontiers of Massively Parallel Computation
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Multilayer VLSI Layout for Interconnection Networks
ICPP '00 Proceedings of the Proceedings of the 2000 International Conference on Parallel Processing
Computational Aspects of VLSI
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
Volumes of 3d drawings of homogenous product graphs
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
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We study 3-dimensional layouts of the hypercube in a 1-active layer and a general model. The problem can be understood as a graph drawing problem in 3D space and was addressed at Graph Drawing 2003 [5]. For both models we prove general lower bounds which relate volumes of layouts to a graph parameter called cutwidth. Then we propose tight bounds on volumes of layouts of N-vertex hypercubes. Especially, we have $ {\rm VOL}_{1-AL}(Q_{\log N})= \frac{2}{3}N^{\frac{3}{2}}\log N +O(N^{\frac{3}{2}}), $ for even log N and ${\rm VOL}(Q_{\log N})=\frac{2\sqrt{6}}{9}N^{\frac{3}{2}}+O(N^{4/3}\log N),$ for log N divisible by 3. The 1-active layer layout can be easily extended to a 2-active layer (bottom and top) layout which improves a result from [5].