论文信息 - Ready, Set, Go! The Voronoi diagram of moving points that start from a line

Ready, Set, Go! The Voronoi diagram of moving points that start from a line

It is an outstanding open problem of computational geometry to prove a near-quadratic upper bound on the number of combinatorial changes in the Voronoi diagram of points moving at a common constant speed along linear trajectories in the plane. In this note we observe that this quantity is Θ(n2) if the points start their movement from a common line.

Vladlen Koltun

[1] J. Sack,et al. Handbook of computational geometry , 2000 .

[2] Raimund Seidel,et al. The Upper Bound Theorem for Polytopes: an Easy Proof of Its Asymptotic Version , 1995, Comput. Geom..

[3] Jon M. Kleinberg,et al. Voronoi Diagrams of Rigidly Moving Sets of Points , 1992, Inf. Process. Lett..

[4] Raimund Seidel,et al. Voronoi diagrams and arrangements , 1985, SCG '85.

[5] Hiroshi Imai,et al. Maximin location of convex objects in a polygon and related dynamic Voronoi diagrams , 1990, SCG '90.

[6] L. Paul Chew,et al. Near-quadratic Bounds for the L1Voronoi Diagram of Moving Points , 1993, Comput. Geom..

[7] Thomas Roos,et al. New Upper Bounds on Voronoi Diagrams of Moving Points , 1997, Nord. J. Comput..

[8] Olivier Devillers,et al. Queries on Voronoi Diagrams of Moving Points , 1996, Comput. Geom..

[9] Richard C. T. Lee,et al. Voronoi Diagrams of Moving Points in the Plane , 1990, FSTTCS.

[10] Leonidas J. Guibas,et al. Data structures for mobile data , 1997, SODA '97.

[11] Leonidas J. Guibas,et al. Voronoi Diagrams of Moving Points , 1998, Int. J. Comput. Geom. Appl..

[12] Micha Sharir,et al. Davenport-Schinzel sequences and their geometric applications , 1995, Handbook of Computational Geometry.

[13] J.. SOME DYNAMIC COMPUTATIONAL GEOMETRY PROBLEMS , 2009 .