Voronoi diagrams of rigidly moving sets of points
Information Processing Letters
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
3-Dimensional Euclidean Voronoi Diagrams of Lines with a Fixed Number of Orientations
SIAM Journal on Computing
Ready, set, go! the Voronoi diagram of moving points that start from a line
Information Processing Letters
A kinetic triangulation scheme for moving points in the plane
Computational Geometry: Theory and Applications
Convex Distance Functions In 3-Space Are Different
Fundamenta Informaticae
Kinetic data structures for all nearest neighbors and closest pair in the plane
Proceedings of the twenty-ninth annual symposium on Computational geometry
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Let P be a collection of n points moving along pseudo-algebraic trajectories in the plane. One of the hardest open problems in combinatorial and computational geometry is to obtain a nearly quadratic upper bound, or at least a subcubic bound, on the maximum number of discrete changes that the Delaunay triangulation DT(P) of P experiences during the motion of the points of P. In this paper we obtain an upper bound of O(n2+ε), for any ε0, under the assumptions that (i) any four points can be co-circular at most twice, and (ii) either no ordered triple of points can be collinear more than once, or no triple of points can be collinear more than twice.