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R.G. Melhem, G.Y. Hwang, "Embedding Rectangular Grids into Square Grids with Dilation Two," IEEE Transactions on Computers, vol. 39, no. 12, pp. 14461455, December, 1990.  
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@article{ 10.1109/12.61064, author = {R.G. Melhem and G.Y. Hwang}, title = {Embedding Rectangular Grids into Square Grids with Dilation Two}, journal ={IEEE Transactions on Computers}, volume = {39}, number = {12}, issn = {00189340}, year = {1990}, pages = {14461455}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.61064}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Embedding Rectangular Grids into Square Grids with Dilation Two IS  12 SN  00189340 SP1446 EP1455 EPD  14461455 A1  R.G. Melhem, A1  G.Y. Hwang, PY  1990 KW  VLSI; multiple ripple propagation technique; mapping; dilation two property; circuit layout CAD; VLSI. VL  39 JA  IEEE Transactions on Computers ER   
A novel technique, the multiple ripple propagation technique, is presented for mapping and h*w grid into a w*h grid such that the dilation cost is 2, i.e. such that any two neighboring nodes in the first grid are mapped onto two nodes in the second grid that are separated by a distance of at most 2. The technique is then used as a basic tool for mapping any rectangular source grid into a square target grid with the dilation two property preserved. The ratio of the number of nodes in the source grid to the number of nodes in the target grid, called the expansion cost, is shown to be always less than 1.2. This is a significant improvement over the previously suggested techniques, where the expansion cost could be bounded by 1.2 only if the dilation cost was allowed to be as high as 18.
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