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Abstract: 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.

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   Matthew T. Dickerson, Robert L. Scot Drysdale, Scott A. McElfresh, and Emo Welzl, "Fast Greedy Triangulation Algorithms." Dartmouth Computer Science Technical Report PCS-TR94-215, 1994.

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