We prove that every tree T = (V, E) on n vertices with edges of unit length can be embedded in the plane with distortion O( √ n); that is, we construct a mapping f: V → R2 suc...
The doubling constant of a metric space (X, d) is the smallest value λ such that every ball in X can be covered by λ balls of half the radius. The doubling dimension of X is the...