The greedy triangulation can be computed from the Delaunay triangulation in linear time

Christos Levcopoulos, Drago Krznaric
1999 Computational geometry  
The greedy triangulation of a finite planar point set is obtained by repeatedly inserting a shortest diagonal that does not cross those already in the plane. The Delaunay triangulation, which is the straight-line dual of the Voronoi diagram, can be produced in O(n log n) worst-case time, and often even faster, by several practical algorithms. In this paper we show that for any planar point set S, if the Delaunay triangulation of S is given, then the greedy triangulation of S can be computed in linear worst-case time (and linear space).
doi:10.1016/s0925-7721(99)00037-1 fatcat:wuhsbwhrqja73ozv255zvsklhe