Fast Algorithms for Greedy Triangulation

We present the first quadratic-time algorithm for the greedy triangulation of a finite planar point set, and the first linear-time algorithm for the greedy triangulation of a convex polygon.

[1]  Leonidas J. Guibas,et al.  A linear-time algorithm for computing the voronoi diagram of a convex polygon , 1989, Discret. Comput. Geom..

[2]  Glenn K. Manacher,et al.  Neither the Greedy Nor the Delaunay Triangulation of a Planar Point Set Approximates the Optimal Triangulation , 1979, Inf. Process. Lett..

[3]  Jörg-Rüdiger Sack,et al.  Heuristics for Optimum Binary Search Trees and Minimum Weight Triangulation Problems , 1989, Theor. Comput. Sci..

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

[5]  Sally A. Goldman A Space Efficient Greedy Triangulation Algorithm , 1989, Inf. Process. Lett..

[6]  Andrzej Lingas Greedy Triangulation acn be Efficiently Implemented in the Average Case (Extended Abstract) , 1988, WG.

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

[8]  Andrzej Lingas A space efficient algorithm for the greedy triangulation , 1988 .

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

[10]  Andrzej Lingas Voronoi Diagrams with Barriers and the Shortest Diagonal Problem , 1989, Inf. Process. Lett..

[11]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

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