Technical Report Number
The greedy triangulation of a set $S$ of $n$ points in the plane is the triangulation obtained by starting with the empty set and at each step adding the shortest compatible edge between two of the points, where a compatible edge is defined to be an edge that crosses none of the previously added edges. In this paper we present a simple, practical algorithm that computes the greedy triangulation in expected time $O(n \log n)$ and space $O(n)$ for points uniformly distributed over any convex shape. A variant of this algorithm should be fast for some other distributions. As part of this algorithm we give an edge compatiblity test that requires $O(n)$ time for both tests and updates to the underlying data structure. We also prove properties about the expected lengths of edges in greedy and Delaunay triangulations of uniformly distributed points.
Dartmouth Digital Commons Citation
Dickerson, Matthew T.; Drysdale, Robert L. Scot; McElfresh, Scott A.; and Welzl, Emo, "Fast Greedy Triangulation Algorithms" (1994). Computer Science Technical Report PCS-TR94-215. https://digitalcommons.dartmouth.edu/cs_tr/92