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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.
Bibliographic citation for this report: [plain text] [BIB] [BibTeX] [Refer]
Or copy and paste:
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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