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 \| ⋅ log ⁡ \| V \| ) {\displaystyle O(\|V\|\cdot \log \|V\|)}
Best-case performance	O ( \| V \| ) {\displaystyle O(\|V\|)}

The greedy triangulation is a method to compute a polygon triangulation or a point set triangulation using a greedy algorithm, 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.¹²

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{{citation}}: CS1 maint: multiple names: authors list (link)

[Loera2010-1] 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.

[bkos-2] Mark de Berg, Marc van Kreveld, Mark Overmars, and Otfried Schwarzkopf (2000), Computational Geometry (2nd revised ed.), Springer-Verlag, ISBN 3-540-65620-0{{citation}}: CS1 maint: multiple names: authors list (link)

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