A Space Efficient Greedy Triangulation Algorithm

Abstract We show that the greedy triangulation of n points in the plane can be computed in O(n2 log (n) time and O(n) memory and storage. In particular we show that, by maintaining a generalized Delaunay triangulation, the next edge to be added to the greedy triangulation can be found in O(n) time. Furthermore, if the generalized Delaunay triangulation of a simple polygon could be computed in O(n) time, our algorithm would compute the greedy triangulation in O(n2) time.

[1]  Errol L. Lloyd.  On triangulations of a set of points in the plane , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[2]  Leonidas J. Guibas,et al.  A linear-time algorithm for computing the voronoi diagram of a convex polygon , 1987, Discret. Comput. Geom..

[3]  Christos Levcopoulos.  An \Omega(\sqrt(n)) Lower Bound for the Nonoptimality of the Greedy Triangulation , 1987, Inf. Process. Lett..

[4]  Michael Ian Shamos,et al.  Closest-point problems , 1975, 16th Annual Symposium on Foundations of Computer Science (sfcs 1975).

[5]  Peter Gilbert.  New Results on Planar Triangulations. , 1979 .

[6]  D. T. Lee,et al.  Generalized delaunay triangulation for planar graphs , 1986, Discret. Comput. Geom..

[7]  Lenhart K. Schubert,et al.  An optimal algorithm for constructing the Delaunay triangulation of a set of line segments , 1987, SCG '87.