Splitting a Delaunay Triangulation in Linear Time

@article{Chazelle2002SplittingAD,
  title={Splitting a Delaunay Triangulation in Linear Time},
  author={Bernard Chazelle and Olivier Devillers and Ferran Hurtado and Merc{\`e} Mora and Vera Sacrist{\'a}n Adinolfi and Monique Teillaud},
  journal={Algorithmica},
  year={2002},
  volume={34},
  pages={39-46}
}
Computing the Delaunay triangulation of n points requires usually a minimum of Ω(n log n) operations, but in some special cases where some additional knowledge is provided, faster algorithms can be designed. Given two sets of points, we prove that, if the Delaunay triangulation of all the points is known, the Delaunay triangulation of each set can be computed in randomized expected linear time. 
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