TY - GEN

T1 - On topological changes in the Delaunay triangulation of moving points

AU - Rubin, Natan

PY - 2012/7/23

Y1 - 2012/7/23

N2 - Let P be a collection of n points moving along pseudo-algebraic trajectories in the plane. 1 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(n 2+ε), for any ε > 0, 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.

AB - Let P be a collection of n points moving along pseudo-algebraic trajectories in the plane. 1 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(n 2+ε), for any ε > 0, 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.

KW - Delaunay triangulation

KW - Discrete changes

KW - Kinetic algorithms

KW - Moving points

KW - Voronoi diagram

UR - http://www.scopus.com/inward/record.url?scp=84863896096&partnerID=8YFLogxK

U2 - https://doi.org/10.1145/2261250.2261252

DO - https://doi.org/10.1145/2261250.2261252

M3 - Conference contribution

SN - 9781450312998

T3 - Proceedings of the Annual Symposium on Computational Geometry

SP - 1

EP - 10

BT - Proceedings of the 28th Annual Symposuim on Computational Geometry, SCG 2012

T2 - 28th Annual Symposuim on Computational Geometry, SCG 2012

Y2 - 17 June 2012 through 20 June 2012

ER -