  Let S be a planar point set. Krznaric and Levcopoulos proved that given the
Delaunay triangulation DT(S) for S, one can find the greedy triangulation GT(S)
in linear time. We provide a (partial) converse of this result: given GT(S), it
is possible to compute DT(S) in linear expected time. Thus, these structures
are basically equivalent.
  To obtain our result, we generalize another algorithm by Krznaric and
Levcopoulos to find a hierarchical clustering for S in linear time, once DT(S)
is known. We show that their algorithm remains (almost) correct for any
triangulation of bounded dilation, i.e., any triangulation in which the
shortest path distance between any two points approximates their Euclidean
distance. In general, however, the resulting running time may be superlinear.
Nonetheless, we can show that the properties of the greedy triangulation
suffice to guarantee a linear time bound.
