On Embeddings of Rectangles into Optimal Squares

Let G = h x w be a rectangular grid and H = s x s be the optimal sqaure grid for G, i.e., the least square grid which is no less than G in size. In this paper, an embedding scheme is presented for embedding G into H such that the dilation cost is at most 6. The significance of this result is that optimal expansion is always achieved, regardless of the aspect ratio of the rectangle, while keeping the dilation constant.