Metric Embedding Two metric spaces:(X,dx)and (Y,dy) (X,dx) (Y,d) low-distortion:for small a 1 x1,2∈X:-dxx1,x2)≤dy((x1),(x2》≤adxx1,x2)Metric Embedding low-distortion: for small α ≥ 1 ∀x1, x2 ∈ X : 1 α dX(x1, x2) ≤ dY(ϕ(x1), ϕ(x2)) ≤ αdX(x1, x2) ϕ (X, dX) (Y, dY) • Two metric spaces: (X, d and X) (Y, dY)