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On Embedding Rectangular Grids in Hypercubes
October 1988 (vol. 37 no. 10)
pp. 1285-1288
The following graph-embedding question is addressed: given a two-dimensional grid and the smallest hypercube with at least as many nodes as grid points, how can one assign grid points to hypercube nodes (with at most one grid point per node) so as to keep grid neighbors near each other in the cube? An embedding scheme for an infinite class of two-dimensional grids is given that keeps grid neigh

[1] J. E. Brandenburg and D. S. Scott, "Embeddings of communication trees and grids into hypercubes," Intel Scientif. Comput. Scientif. Rep. 280182-001, 1985.
[2] T. F. Chan and F. Chin, private communications, 1985.
[3] S. N. Bhatt, F. R. K. Chung, T. Leighton, and A. L. Rosenburg, "Optimal embeddings of binary trees in the Boolean hypercube," Res. Rep. in preparation, Dep. Comput. Sci., Yale Univ.
[4] S. N. Bhatt and I. C. F. Ipsen, "How to embed trees in hypercubes," Res. Rep. 443, Dep. Comput. Sci., Yale Univ., Dec. 1985.
[5] Y. Saad and M. H. Schultz, "Topological properties of hypercubes," Res. Rep. 389, Dep. Comput. Sci., Yale Univ., June 1985.

Index Terms:
embedding rectangular grids; hypercubes; grid neighbors; two-dimensional grids; graph theory; multiprocessing systems.
Citation:
M.Y. Chan, F.Y.L. Chin, "On Embedding Rectangular Grids in Hypercubes," IEEE Transactions on Computers, vol. 37, no. 10, pp. 1285-1288, Oct. 1988, doi:10.1109/12.5991
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