Greedy triangulation

Greedy triangulation
Polygon Greedy triangulation steps. On each step a new edge (red) is added joining the nearest pair of vertex, without crossing a previously edge
Class	Search algorithm
Data structure	Priority queue Spatial database
Worst-case performance	$O(\|V\|\cdot \log \|V\|)$
Best-case performance	$O(\|V\|)$

The Greedy Triangulation is a method to compute a polygon triangulation or a Point set triangulation using a greedy schema, which adds edges one by one to the solution in strict increasing order by length, with the condition that an edge cannot cut a previously inserted edge. ^[1] ^[2]

References

↑ J. Loera, J. Rambau and F. Santos (2010), Triangulations: Structures and Algorithms (2nd revised ed.), Springer-Verlag, ISBN 9783642129711 Chapter 3: Polygon Triangulation: pp.103.
↑ Mark de Berg, Marc van Kreveld, Mark Overmars, and Otfried Schwarzkopf (2000), Computational Geometry (2nd revised ed.), Springer-Verlag, ISBN 3-540-65620-0

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