Embedding between 2-D meshes of the same size

It is shown how to embed an x₁ × 1₁ mesh M₁ into an s₂ × t₂ mesh M ₂, where s₁ × t₂, s₁ < t_i (i = 1,2) such that the dilation is minimized. It is assumed that load = 1 and expansion = 1. For each case there is shown a lower bound on the dilation and a corresponding embedding method. The dilations by these embedding algorithms either match a lower bound or are very close to a lower bound